e) \(8^n:2^n=4\)
\(\Rightarrow\left(8:2\right)^n=4\)
\(\Rightarrow4^n=4\)
\(\Rightarrow n=1\)
f) \(\left(\dfrac{9}{5}\right)^n.\left(\dfrac{5}{4}\right)^n=\left(\dfrac{3}{2}\right)^{10}\)
\(\Rightarrow\left(\dfrac{9}{5}\cdot\dfrac{5}{4}\right)^n=\left(\dfrac{3}{2}\right)^{10}\)
\(\Rightarrow\left(\dfrac{9}{4}\right)^n=\left(\dfrac{3}{2}\right)^{10}\)
\(\Rightarrow\left[\left(\dfrac{3}{2}\right)^2\right]^n=\left(\dfrac{3}{2}\right)^{10}\)
\(\Rightarrow\left(\dfrac{3}{2}\right)^{2n}=\left(\dfrac{3}{2}\right)^{10}\)
\(\Rightarrow2n=10\)
\(\Rightarrow n=5\)
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