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How to simplify it? [ log5(8)*log2{sqrt(10)}] / log25{10} ]?
[log5(8)*log2{sqrt(10)}] / log25{10}
2 Answers
- ted sLv 71 decade agoFavorite Answer
go to natural logs
log {base 5} 8 = 3 ln2 / ln 5 , log {base 2} √10 = ln 10 / 2 ln 2 ,
log {base 25} 10 = ln 10 / 2 ln 5
{ 3 ln2 ln10 / [ln5 (2ln2) ] } / [ln 10 / 2 ln5] =
{ 3 ln 2 (ln 10 )[2 ln 5] } / { ln 5 ( 2 ln 2)[ln 10] }
= 3
- peabodyLv 71 decade ago
[log5(8)*log2{sqrt(10)}] / log25{10}
= [ log 8 / log 5 * log 10^1/2 / log 2 ] / (log 10 / log 25) ///// all to base 10
= [ log 8 / log 5 * log 10^1/2 / log 2 ] * log 25 /log10
= ( log 8 * log 10^1/2 * log 25) / ( log 5 * log 2 * log 10)
= log ( 8 *10^1/2*25) / log (5*2*10)
= log ( 200 *10^1/2) / log ( 100)
= = log ( 2 * 10^2 * 10^1/2 ) / log 10^2
= log ( 2 * 10 ^5/2) / log 10^2
= [ log 2 + log 10^5/2] / 2log 10
= log 2 / 2 + (5/2 ) / 2
= 1/2 log 2 + 5/4
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