#1619 · Real Analysis · Series

Logarithms of Small Primes

If $lo g_{e} \frac{9}{10} = - a$ , $lo g_{e} \frac{24}{25} = - b$ , $lo g_{e} \frac{81}{80} = c$ , shew that $lo g_{e} 2 = 7 a - 2 b + 3 c$ , $lo g_{e} 3 = 11 a - 3 b + 5 c$ , $lo g_{e} 5 = 16 a - 4 b + 7 c$ ; and calculate $lo g_{e} 2$ , $lo g_{e} 3$ , $lo g_{e} 5$ to 8 places of decimals.

~25 minAnswer checked instantlyLogarithmsDecimal approximations

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XVII. Exponential and Logarithmic Series, Examples XVII, No. 24

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).