Giải:
a) \(\dfrac{32}{2^n}=4\)
\(\Leftrightarrow2^n=\dfrac{32}{4}\)
\(\Leftrightarrow2^n=8\)
\(\Leftrightarrow2^n=2^3\)
Vì \(2=2\)
Nên \(n=3\).
b) \(\dfrac{625}{5^n}=5\)
\(\Leftrightarrow5^n=\dfrac{625}{5}\)
\(\Leftrightarrow5^n=125\)
\(\Leftrightarrow5^n=5^3\)
Vì \(5=5\)
Nên \(n=3\).
c) \(\dfrac{27^n}{3^n}=3^2\)
\(\Leftrightarrow\dfrac{\left(3^3\right)^n}{3^n}=3^2\)
\(\Leftrightarrow\dfrac{3^{3n}}{3^n}=3^2\)
\(\Leftrightarrow3^{3n}=3^n.3^2\)
\(\Leftrightarrow3^{3n}=3^{n+2}\)
Vì \(3=3\)
Nên \(3n=n+2\)
\(\Leftrightarrow3n-n=2\)
\(\Leftrightarrow2n=2\)
\(\Leftrightarrow n=1\).
Chúc bạn học tốt!
