Solve for x :
log 64log 8\dfrac{\text{log 64}}{\text{log 8}}log 8log 64 = log x
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Given,
⇒log 64log 8=log x⇒log 26log 23=log x⇒6 log 23 log 2=log x⇒log x=2⇒x=102=100.\Rightarrow \dfrac{\text{log 64}}{\text{log 8}} = \text{log x} \\[1em] \Rightarrow \dfrac{\text{log 2}^6}{\text{log 2}^3} = \text{log x} \\[1em] \Rightarrow \dfrac{\text{6 log 2}}{\text{3 log 2}} = \text{log x} \\[1em] \Rightarrow \text{log x} = 2 \\[1em] \Rightarrow x = 10^2 = 100.⇒log 8log 64=log x⇒log 23log 26=log x⇒3 log 26 log 2=log x⇒log x=2⇒x=102=100.
Hence, x = 100.
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log 81log 27\dfrac{\text{log 81}}{\text{log 27}}log 27log 81 = x
log 128log 32\dfrac{\text{log 128}}{\text{log 32}}log 32log 128 = x
log 225log 15\dfrac{\text{log 225}}{\text{log 15}}log 15log 225 = log x
Given log x = m + n and log y = m - n, express the value of log 10xy2\dfrac{10x}{y^2}y210x in terms of m and n.
