Lemma

Algebra · Chapter 13 of 20

Exponentials & logarithms

153 curated · 715 from open sources · 73,026 generated

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Evaluate a logarithmEasy · 1,026 variationsExponential equationMedium · 72,000 variations

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153
#TitleDifficultySourceTags
759A logarithmEasyLemmaExponentials & logarithms
760Match the basesEasyLemmaExponentials & logarithms
762Inverse functions cancelEasyLemmaExponentials & logarithms
1133Rationalize the denominator with three termsEasyHall & Knightrationalizing the denominatorsurds
1141Rationalising Factor for a Cube Root BinomialEasyHall & Knightsurdsdifference of cubes
1149Square Root of Surd ExpressionEasyHall & Knightsurdssquare root
1150Square Root of Surd ExpressionEasyHall & Knightsurdssquare root
1151Square Root of Surd ExpressionEasyHall & Knightsurdssquare root
1155Cube Root of a SurdEasyHall & Knightsurdscube roots
1156Cube Root of a SurdEasyHall & Knightsurdscube roots
1157Cube Root of a SurdEasyHall & Knightsurdscube roots
1161Square root of a binomial surdEasyHall & Knightsurdssquare root
1165Evaluate expression with surd valuesEasyHall & Knightrationalizationalgebraic evaluation
1166Evaluate symmetric rational expressionEasyHall & Knightrationalizationalgebraic evaluation
1169Difference of Surd PowersEasyHall & KnightSurdsSquare roots+1
1261Exponential Equation in Base 3EasyHall & Knightexponential equationsquadratic form
1262Reciprocal Exponential EquationEasyHall & Knightexponential equationsreciprocals
1263Exponential equation reducible to quadraticEasyHall & Knightexponential equationssubstitution
1265Square root exponential equationEasyHall & Knightexponential equationsreciprocal terms
1294Exponential EquationEasyHall & KnightExponentsExponential equations
1473Approximation Neglecting Higher PowersEasyHall & KnightBinomial TheoremLinear Approximation
1557Logarithm of a power of radicalsEasyHall & Knightlogarithmsproperties of logarithms+1
1558Logarithm of a product of radicalsEasyHall & Knightlogarithmsproperties of logarithms+1
1559Logarithm of a negative power radicalEasyHall & Knightlogarithmsproperties of logarithms
1562Logarithm of an algebraic expressionEasyHall & Knightlogarithm propertiesexponent rules
1568Exponential equation with basesEasyHall & Knightlogarithmsexponential equations
1569Exponential equation quotientsEasyHall & Knightlogarithmsexponential equations
1571Logarithmic systemEasyHall & Knightlogarithm propertiessystems of equations
1573Logarithm of 64EasyHall & Knightlogarithmsproperties of logarithms
1574Logarithm of 84EasyHall & Knightlogarithmsproperties of logarithms
1575Logarithm of a decimalEasyHall & KnightLogarithmsCommon logarithms
1576Logarithm of a mixed decimalEasyHall & KnightLogarithmsCommon logarithms
1577Logarithm of a mixed numberEasyHall & KnightLogarithmsCommon logarithms
1578Logarithm of a cube rootEasyHall & KnightLogarithmsRadicals
1579Logarithm of a square root fractionEasyHall & KnightLogarithmsRadicals
1580Logarithm of a rootEasyHall & KnightLogarithmsProperties of logarithms
1581Seventh root using logarithmsEasyHall & KnightLogarithmsRoots
1582Eleventh root of a powerEasyHall & KnightLogarithmsPowers and roots
1584Logarithm of a fractional radical expressionEasyHall & KnightLogarithmsRadicals
1588Number of digits via logarithmsEasyHall & Knightlogarithmscharacteristic+1
1591Exponential equation with logarithmsEasyHall & Knightlogarithmsexponential equations
1592Exponential equation base fiveEasyHall & Knightlogarithmsexponential equations
1593Exponential equation with two basesEasyHall & Knightlogarithmsexponential equations
1598Logarithm with a Different BaseEasyHall & Knightlogarithmschange of base
1620Compound interest over fifty yearsEasyHall & Knightcompound interestlogarithms
1622Doubling time at compound interestEasyHall & Knightcompound interestlogarithms
1623Present value of a sumEasyHall & Knightpresent valuecompound interest
1624Time to grow to a targetEasyHall & Knightcompound interestlogarithms
1826Logarithm base root twoEasyHall & Knightlogarithmsbase conversion
1827Logarithm base two root threeEasyHall & Knightlogarithmsexponents
1828Logarithm of 125 to base 5 root 5EasyHall & Knightlogarithmspowers of numbers
1829Logarithm of 0.25 to base 4EasyHall & Knightlogarithmsnegative exponents
1831Logarithm of repeating decimal base 9EasyHall & Knightlogarithmsrepeating decimals
1832Logarithm of decimal base 2EasyHall & Knightlogarithmsdecimals
1836Logarithm of root term to base aEasyHall & Knightlogarithmsalgebraic exponents
1837Logarithm of inverse root term to base aEasyHall & Knightlogarithmsnegative exponents
1838Logarithm of cube root of negative power to base aEasyHall & Knightlogarithmsalgebraic exponents
1839Logarithm base 8 of 128EasyHall & Knightlogarithmsexponents
1840Logarithm of a fractionEasyHall & Knightlogarithmsnegative exponents
1841Logarithm base 27EasyHall & Knightlogarithmsfractional bases
1842Logarithm base 343EasyHall & Knightlogarithmspowers of 7
1843Characteristic of 21735EasyHall & Knightlogarithmscharacteristic
1844Characteristic of 23.8EasyHall & Knightlogarithmscharacteristic
1845Characteristic of 350EasyHall & Knightlogarithmscharacteristic
1846Characteristic of .035EasyHall & Knightlogarithmscharacteristic
1847Characteristic of .2EasyHall & Knightlogarithmscharacteristic
1848Characteristic of .87EasyHall & Knightlogarithmscharacteristic
1849Characteristic of .875EasyHall & Knightlogarithmscharacteristic
1850Logarithm of 7.623EasyHall & Knightlogarithmsmantissa+1
1851Logarithm of 762.3EasyHall & Knightlogarithmsmantissa+1
1852Logarithm of .007623EasyHall & Knightlogarithmsmantissa+1
1853Logarithm of 762300EasyHall & Knightlogarithmsmantissa+1
1854Logarithm of .000007623EasyHall & Knightlogarithmsmantissa+1
1855Digits in integer part for 4.30103EasyHall & Knightlogarithmscharacteristic+1
1856Digits in integer part for 1.4771213EasyHall & Knightlogarithmscharacteristic+1
1857Digits in integer part for 3.69897EasyHall & Knightlogarithmscharacteristic+1
1858Digits in integer part for .56515EasyHall & Knightlogarithmscharacteristic+1
1859Position of first significant figure for \bar{2}.7781513EasyHall & Knightlogarithmscharacteristic+1
1860Position of first significant figure for .6910815EasyHall & Knightlogarithmscharacteristic+1
1861Position of first significant figure for \bar{5}.4871384EasyHall & Knightlogarithmscharacteristic+1
1862Logarithm Base Change 1EasyHall & Knightlogarithmsradicals+1
1863Logarithm Base Change 2EasyHall & Knightlogarithmsradicals+1
108Where exponentials crossMediumLemmaLogarithms
761A logarithmic equationMediumLemmaExponentials & logarithms
1134Rationalize denominator involving rootsMediumHall & Knightrationalizing the denominatorsurds
1135Algebraic rationalization of surdsMediumHall & Knightrationalizing the denominatoralgebraic surds
1137Rationalizing a multi-term surd expressionMediumHall & Knightrationalizing the denominatorsurds
1138Simplify and rationalize a product of surdsMediumHall & Knightrationalizing the denominatorsurds
1139Rationalising Factor for Cube and Square RootsMediumHall & Knightsurdsrationalisation
1140Rationalising Factor for Fifth and Third RootsMediumHall & Knightsurdsrationalisation
1142Rationalising Factor for Fourth Roots and IntegersMediumHall & Knightsurdsrationalisation
1143Rationalize Cube Root DenominatorMediumHall & Knightrationalizationsurds+1
1146Rationalizing with Sixth RootsMediumHall & Knightrationalizationsurds
1148Rationalize Sixth Root of 27MediumHall & Knightrationalizationsurds
1152Square Root of Surd ExpressionMediumHall & Knightsurdssquare root
1153Square Root of Algebraic SurdMediumHall & Knightsurdssquare root
1158Cube Root of a SurdMediumHall & Knightsurdscube roots
1159Cube Root of a SurdMediumHall & Knightsurdscube roots
1160Cube Root of a SurdMediumHall & Knightsurdscube roots
1162Square root of a radical expressionMediumHall & Knightsurdssquare root
1163Square root with higher powersMediumHall & Knightsurdsalgebraic manipulation
1164Square root of algebraic sumMediumHall & Knightsurdsradicals
1167Simplifying a Nested Radical ExpressionMediumHall & KnightSurdsRationalization+1
1168Square Root of a Fraction with SurdsMediumHall & KnightSurdsRationalization+1
1170Binomial Cube Roots and Fractional PowersMediumHall & KnightSurdsCube roots+1
1171Numerical Evaluation with Given Square RootMediumHall & KnightSurdsRationalization+1
1173Cube Root of a Binomial SurdMediumHall & KnightSurdsCube roots
1174Rationalizing and Evaluating Surd ExpressionMediumHall & KnightSurdsRationalization
1255Exponential parameter equationMediumHall & Knightexponentsquadratic substitution
1256Exponential equation with variable powerMediumHall & Knightsubstitutionexponents
1264Exponential equation with powers of 2MediumHall & Knightexponential equationsquadratic form
1266Fractional exponential equationMediumHall & Knightexponential equationsrational coefficients
1295Exponential Parameter EquationMediumHall & KnightExponentsFactoring
1471Decimal Value of Fractional PowerMediumHall & KnightBinomial TheoremApproximation
1472Fifth Root ApproximationMediumHall & KnightBinomial TheoremRoots
1474Square Root and Reciprocal ApproximationMediumHall & KnightBinomial TheoremLinear Approximation
1475Fractional Binomial ApproximationMediumHall & KnightBinomial TheoremFractions
1476Complex Algebraic ApproximationMediumHall & KnightBinomial TheoremApproximation
1501Surd Power Fractional Part PropertyMediumHall & KnightSurdsBinomial Expansion
1560Logarithm of a product of compound radicalsMediumHall & Knightlogarithmsexponents
1563Simplifying a logarithmic expressionMediumHall & Knightlogarithm propertiessimplification
1564Logarithmic identity proofMediumHall & Knightlogarithm propertiesprime factorization
1565Simplify a nested radical logarithmMediumHall & Knightlogarithm propertiespowers of a base
1566Prove a logarithmic relationMediumHall & Knightlogarithm propertiescombining logarithms
1567Solve an exponential equationMediumHall & Knightexponential equationslogarithms
1570System of exponential equationsMediumHall & Knightlogarithmssystems of equations
1572Prove an exponential relationMediumHall & Knightlogarithmsproof
1583Product of decimal numbersMediumHall & KnightLogarithmsMultiplication via logarithms
1585Logarithm of a combined radical expressionMediumHall & KnightLogarithmsSimplification
1586Logarithmic evaluation of a rootMediumHall & Knightlogarithmsexponentiation+1
1587Logarithmic calculation with radicalsMediumHall & Knightlogarithmsfractional powers+1
1589Inequality with large powersMediumHall & Knightlogarithmsinequalities
1590Leading zeros of small powersMediumHall & Knightlogarithmsdecimals+1
1594Exponential equation with decimalsMediumHall & Knightlogarithmsexponential equations
1595Complex exponential equationMediumHall & Knightlogarithmsexponential equations
1596Simultaneous exponential equations IMediumHall & Knightsimultaneous equationslogarithms
1597Simultaneous exponential equations IIMediumHall & Knightsimultaneous equationslogarithms
1621Simple interest and discountMediumHall & Knightsimple interestdiscount
1625Discount as harmonic meanMediumHall & Knightsimple interestharmonic mean+1
1626Century of Compound InterestMediumHall & Knightcompound interestlogarithms
1627Present Value at Compound InterestMediumHall & Knightcompound interestpresent value
1637Continuously Compounded AmountMediumHall & Knightcontinuous compoundingexponential growth
1830Logarithm of a fraction base 2 root 2MediumHall & Knightlogarithmsfractional exponents
1833Logarithm of 1000 base 0.01MediumHall & Knightlogarithmspowers of 10
1834Logarithm of 0.0001 base 0.001MediumHall & Knightlogarithmspowers of 10
1835Logarithm of repeating decimal base 9 root 3MediumHall & Knightlogarithmsrepeating decimals
1136Rationalize a complex surd fractionDeepHall & Knightrationalizing the denominatorsurds
1144Rationalize Sixth Root DenominatorDeepHall & Knightrationalizationsurds+1
1145Rationalize Mixed Radical DenominatorDeepHall & Knightrationalizationsurds
1147Rationalize Difference of Square and Cube RootsDeepHall & Knightrationalizationsurds+1
1154Square Root of Complex SurdDeepHall & Knightsurdssquare root
1561Logarithm of a quotient of nested radicalsDeepHall & Knightlogarithmsnested radicals
1628Accumulation of a FarthingDeepHall & Knightcompound interesthistorical currency

From open sources

715

Complete problems only, with worked solutions first. Show everything

#TitleDifficultySource
11129A certain kind of wild mushroom has either spots or gills, but…EasyGSM8K
12842Dolly wants to ride the Ferris wheel twice, the roller coaster three…DeepGSM8K
12897John takes a 20-foot log and cuts it in halfEasyGSM8K
13733David finished his homework in 60 minutesEasyGSM8K
15393Marcy can make 3 spears out of a sapling and 9 spears…EasyGSM8K
16455A group of nine turtles sat on a logMediumGSM8K
16864A lumberjack is chopping down trees so he can sell firewoodEasyGSM8K
19210Which of the following statements is not correctMediumAQuA
19228log(a(a(a)^1/4)^1/4)^1/4 here base is aMediumAQuA
20837Find the value of log y(x4) if logx(y3) = 2MediumAQuA
22592If log X/2=log Y/3 = log Z/5, then YZ in terms of…MediumAQuA
22595The value of log 5 (1/125) isMediumAQuA
22923If x>=y and y>1 , what is the maximum value of log…MediumAQuA
25192If log 27 = 1.431, then the value of log 9 is:0.934…MediumAQuA
29332If Log2 x - 5 Log x + 6 = 0, then…MediumAQuA
33921If log 32 x= 0.8, then x is equal toMediumAQuA
36865If (0.2)x = 2 and log 2 = 0.3010, then Find the…MediumAQuA
37953If ( log 5 5) (log 4 9) (log 3 2) is…MediumAQuA
41797If f(x) = Log(x), then f -1(x) =MediumAQuA
45304If log 0.318=0.3364 and log 0.317=0.33320 then log 0.319 =MediumAQuA
47145log xy3 = a; log x2y = b then then value of…MediumAQuA
48460If (0.2)x = 2 and log 2 = 0.3010, then the value…MediumAQuA
48822How many 3-letter words with or without meaning, can be formed out…MediumAQuA
49376If log a/b + log b/a= log (a + b), thenMediumAQuA
55022Find the Value of X :log(x+1) + (log(x-1) = log8MediumAQuA
56979log 3600 is equal toMediumAQuA
59067log base 10 root of 10 root of 10 root of 10..........infinityMediumAQuA
64108If log x + log y = log (x+y), thenMediumAQuA
66185If log 2 = 0.3010 and log 3 = 0.4771, the value…MediumAQuA
66680Solve for X, log10X + log√10 X + log3√100 X = 27MediumAQuA
67897If log 64 = 1.8061, then the value of log 16 will…MediumAQuA
70456If log 2 = 0.3010 and log 3 = 0.4771 then the…MediumAQuA
71654If logX/(a2 + ab + b2) = log Y/(b2 + bc +…MediumAQuA
72881If log√8 x = 3×1/3, find the value of xMediumAQuA
73258What is the characteristic of the logarithm of 0.0000134MediumAQuA
75295If log 0.317 = 0.3332 and log 0.318 = 0.3364, then find…MediumAQuA
75339What is the value of m and n MediumAQuA
77964WHAT WILL BE THE VALUE OF log e(e(e....)^1/2)^1/2)^1/2).....log base is eMediumAQuA
78353The volume of the greatest sphere that can be cut off from…MediumAQuA
80490The mantissa of log 3274 is 0.5150MediumAQuA
82464If log(2a - 3b) = log a - log b, then a…MediumAQuA
83616Simplify :(log 75/16-2 log 5/9+log 32/243)MediumAQuA
86124If log 27 = 1.431, then the value of log 9 isMediumAQuA
86223log√ 8 / log 8 is equal toMediumAQuA
86313If log8 x + log 8 1/6 = 1/3, then the value…MediumAQuA
88427If Log 4 (x) = 12, then log 2 (x / 4)…MediumAQuA
88431loga (ab) = x, then log b (ab) is MediumAQuA
92769If log 2 = 0.3010 and log 3 = 0.4771, the value…MediumAQuA
98754If log 2 = 0.3010 and log 3 = 0.4771, the values…MediumAQuA
102366Exponential Functions · Example 1EasyOpenStax
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