Solve for x:
x = log 125log 25\dfrac{\text{log 125}}{\text{log 25}}log 25log 125
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Given,
⇒x=log 125log 25⇒x=log 53log 52⇒x=3log 52log 5⇒x=32.\Rightarrow x = \dfrac{\text{log 125}}{\text{log 25}} \\[1em] \Rightarrow x = \dfrac{\text{log 5}^3}{\text{log 5}^2} \\[1em] \Rightarrow x = \dfrac{\text{3log 5}}{\text{2log 5}} \\[1em] \Rightarrow x = \dfrac{3}{2}.⇒x=log 25log 125⇒x=log 52log 53⇒x=2log 53log 5⇒x=23.
Hence, x = 32\dfrac{3}{2}23.
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log x + log 5 = 2log 3
log3x - log32 = 1
log 8log 2×log 3log3=2logx\dfrac{\text{log 8}}{\text{log 2}} \times \dfrac{\text{log 3}}{\text{log}\sqrt{3}} = 2\text{log} xlog 2log 8×log3log 3=2logx
Given 2log10x + 1 = log10250, find
(i) x
(ii) log102x
