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Algebra · Chapter 13 of 20

Exponentials & logarithms

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#TitleDifficultySourceTags
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

From open sources

306

Complete problems only, with worked solutions first. Show everything

#TitleDifficultySource
16455A group of nine turtles sat on a logMediumGSM8K
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
102399Exponential Functions · Exercise 14MediumOpenStax
102401Exponential Functions · Exercise 16MediumOpenStax
102403Exponential Functions · Exercise 18MediumOpenStax
102405Exponential Functions · Exercise 20MediumOpenStax
102409Exponential Functions · Exercise 24MediumOpenStax
102411Exponential Functions · Exercise 26MediumOpenStax
102415Exponential Functions · Exercise 30MediumOpenStax
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