Question

if log2base10=0.3010 then log25base8=

Answer 1

log25base8 can be written as 2/3 log5base2
                                         
                but we kknow that log2base10=1/log5*2base2

                                                            =1/log5base2+1
upon simplification we get log5base2=2.32

there for log25base8=2/3*2.32=1.564

Answer 2

$log_{8}25 = log_{2^3}5^2 = \frac{2}{3} log_{2} 5$

$\frac{2}{3} log_{2} 5 = \frac{2}{3} \frac{log_{10}5}{log_{10}2}$

$= \frac{2}{3} \frac{log_{10}10 - log_{10}2}{log_{10}2}$

Now substitute the value of $log_{10}2 = 0.3010$

$= \frac{2}{3}* \frac{1- 0.3010}{0.3010}$

$= \frac{2}{3}* \frac{0.699}{0.301}$

 = 0.666 * 2.322

= 1.5464

$log_{8}25 = 1.5464$