Solve for x: 81 27 =x - Vidyadip

Question

Solve for $\mathbf{x}: \frac{\log 81}{\log 27}=x$

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Answer

$ \frac{\log 81}{\log 27}=\mathrm{x}$
$ \Rightarrow \mathrm{x}=\frac{\log 81}{\log 27}$
$ \Rightarrow \mathrm{x}=\frac{\log 3 \times 3 \times 3 \times 3}{\log 3 \times 3 \times 3}$
$ \Rightarrow \mathrm{x}=\frac{\log 3^4}{\log 3^3}$
$ \Rightarrow \mathrm{x}=\frac{4 \log 3}{3 \log 3} \ldots\left[\mathrm{n} \log _{\mathrm{a}} \mathrm{m}=\log _{\mathrm{a}} \mathrm{m}^{\mathrm{n}}\right]$
$ \Rightarrow \mathrm{x}=\frac{4}{3}$
$ \Rightarrow \mathrm{x}=1 \frac{1}{3}$

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