Solve for x :
log 81log 27\dfrac{\text{log 81}}{\text{log 27}}log 27log 81 = x
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Given,
⇒log 81log 27=x⇒log 34log 33=x⇒4 log 33 log 3=x⇒x=43=113.\Rightarrow \dfrac{\text{log 81}}{\text{log 27}} = x \\[1em] \Rightarrow \dfrac{\text{log 3}^4}{\text{log 3}^3} = x \\[1em] \Rightarrow \dfrac{\text{4 log 3}}{\text{3 log 3}} = x \\[1em] \Rightarrow x = \dfrac{4}{3} = 1\dfrac{1}{3}.⇒log 27log 81=x⇒log 33log 34=x⇒3 log 34 log 3=x⇒x=34=131.
Hence, x = 1131\dfrac{1}{3}131.
Answered By
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log (x - 2) + log (x + 2) = log 5
log (x + 5) + log (x - 5) = 4 log 2 + 2 log 3
log 128log 32\dfrac{\text{log 128}}{\text{log 32}}log 32log 128 = x
log 64log 8\dfrac{\text{log 64}}{\text{log 8}}log 8log 64 = log x
