Question
Solve for $\mathbf{x}: \frac{\log 128}{\log 32}=x$
✓
Answer
$ \frac{\log 128}{\log 32}=\mathrm{x}$
$ \Rightarrow x=\frac{\log 128}{\log 32}$
$ \Rightarrow x=\frac{\log 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}{\log 2 \times 2 \times 2 \times 2 \times 2}$
$ \Rightarrow x=\frac{\log 2^7}{\log 2^5}$
$ \Rightarrow x=\frac{7 \log 2}{5 \log 2} \ldots\left[\mathrm{n} \log _{\mathrm{a}} \mathrm{m}=\log _{\mathrm{a}} \mathrm{m}^{\mathrm{n}}\right]$
$ \Rightarrow x=\frac{7}{5}$
$ \Rightarrow \mathrm{x}=1.4$
$ \Rightarrow x=\frac{\log 128}{\log 32}$
$ \Rightarrow x=\frac{\log 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}{\log 2 \times 2 \times 2 \times 2 \times 2}$
$ \Rightarrow x=\frac{\log 2^7}{\log 2^5}$
$ \Rightarrow x=\frac{7 \log 2}{5 \log 2} \ldots\left[\mathrm{n} \log _{\mathrm{a}} \mathrm{m}=\log _{\mathrm{a}} \mathrm{m}^{\mathrm{n}}\right]$
$ \Rightarrow x=\frac{7}{5}$
$ \Rightarrow \mathrm{x}=1.4$
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