Question

25. The value of log 25 to the base 8 ,given log 2 = 0.3010 is
(a) 1
(b) 2
(c) 1.5482​

Answer 1

Answer:

The value of log 25 to the base 8 ,given log 2 = 0.3010 is

(c) 1.5482

Answer 2

Solution:-

therefore, log 2 (to base 10) X log10 (to base 2)

= 1 => log10 (to base 2) = 1/ (log 2 (to base 10) = 1/0.3010 = 3.322

=>log2(to base2)+ log 5(to base2) = 3.322

=>1+ log 5(to base2)=3.322 => log 5(to base2)=3.322-1=2.322

We have another formula: LogA (to base^p) = {logA (to base)}/p

using this formula, log 5(to base 8) = log 5(to base 2^3) = {log 5(to base2)}/3 = 2.322/3 =0.774

now,

log25(to base 8) = log 5^2(to base8)

= 2Xlog5(to base 8)

=2X0.774

=1.54.

Option c is correct