Question

Find the value of log 25 to the base 8 if log2 to the base 10 = 0.3010

Answer 1

Identities used:

1. loga (b) = 1 / logb (a)

2. n*log x = log xn

-

log8 (25) = log8 (100/4) = log8 (100) - log8(4)

log8 (102) - log8(4)

2*log8 (10) - log8(4)

Now log8(10) = 1/ log10(8), also log8(4) = 2/3

-

2 / log10 (8) - 2/3

2 / log10 (23) - 2/3

2 / 3*log10 (2) - 2/3

2/ 3 x 0.3010 - 0.667

2/ 0.903 - 0.667

2.2148 - 0.667

= 1.548