Question 9

Find the value of $$\log_{3^2}{5^4} \times \log_{5^2}{3^4}$$

Solution

$$\log_{b^n}\left(a^m\right)\ =\frac{m}{n}\log_ba\ =\frac{m}{n}\cdot\frac{\log\left(a\right)}{\log\left(b\right)}$$

So given equation becomes $$\frac{4}{2}\cdot\frac{4}{2}\cdot\frac{\log\left(3\right)}{\log\left(2\right)}\cdot\frac{\log\left(2\right)}{\log\left(3\right)}$$ = 4

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