Question 28486: log(3x)= 2.7logx
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! log(3x) = 2.7 logx
log (3x) = log3 + logx
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this is easy to prove
say you're using logs to the base 10
log(10 * 10 * 10) = log 1000 = 3
but also
log10 + log10 + log10 = 3
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log3 + logx = 2.7 logx
subtract logx from both sides
log3 = 2.7 logx - logx
log3 = 1.7 logx
log3 = logx^1.7
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I know this last step is true because
3log(1000) = 3 * 3 = 9
and
log(1000)^3 = log(1000 * 1000 * 1000) = log(1000000000) = 9
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3 = x^1.7
raise each side to the 1/1.7 power
3^(1/1.7) = x^(1.7/1.7)
because x^1 = x
3^(1/1.7) = x answer
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