Question

Evaluate: `(log_5 8)/(log_25 16 xx Log_100 10)` 

Answer 1

`(log_5 8)/(log_25 16 xx log_100 10)` 

= `( log_10 8/ log_10 5)/(log_10 16/log_10 25 xx log_10 10/ log_10 100)`

= `( log_10 2^3/ log_10 5)/(log_10 2^4/log_10 5^2 xx log_10 10/ log_10 10^2)`

= `log_10 2^3/log_10 5 xx log_10 5^2/ log_10 2^4 xx log_10 10^2/ log_10 10 `

= `[3log_10 2]/log_10 5 xx [2log_10 5]/ [4log_10 2] xx[2log_10 10]/ [log_10 10] `

= 3