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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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