Solve for x : 225 15 = x - Vidyadip

Question

Solve for $x :\frac{\log 225}{\log 15}=\log x$

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Answer

$ \Rightarrow \log x=\frac{\log 225}{\log 15}$
$ \Rightarrow \log x=\frac{\log 15 \times 15}{\log 15}$
$ \Rightarrow \log x=\frac{\log 15^2}{\log 15}$
$ \Rightarrow \log x=\frac{2 \log 15}{\log 15} \ldots\left[n \log _a m=\log _a m^n\right]$
$ \Rightarrow \log x=2$
$ \Rightarrow \log _{10} x=2$
$ \Rightarrow 10^2=x$
$ \Rightarrow x=10 \times 10$
$ \Rightarrow x=100$

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