Question

Given log2 base 10=0.3010
Find value of log 25base 8

Answer 1

HEY MATE HERE IS YOUR ANSWER!!!

IDENTITIES USED:-
1.log( 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/log 10(8),also,log(8)4
=2/3.

=2/log 10(8)-2/3

=2/log 10(23)-2/3

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

=2/3 ×0.3010-0.667

=2/0.903-0.667

=2.2148-0.667

=1.548.....