prove that:log25+log8*log16/log64 -log14/5+log28=3

4 answers

put it in your calculator and see if it works
i donot have calculator now
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log8 * log16/log64
= log 2^3 * log 2^4 / log 2^6
= 3log2 * 4log2 / 6log2
= 2log2
= log 4

log (14/5) = log14 - log 5
and log 25 = log 5^2 = 2log 5

so
log25+log8*log16/log64 -log14/5+log28
= log 25 + log 4 - (log14 - log5) + log 28
= log(25*4/14*5 * 28)
= log 1000
= 3
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