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