Đáp án+Giải thích các bước giải:

e)

\(2^{x-1}+2^{x+2}=72\)
\(\frac{2^{x}}{2}+2^{x}\cdot 2^{2}=72\)
\(2^{x}\cdot \frac{1}{2}+2^{x}\cdot 4=72\)
\(2^{x}\cdot \left(\frac{1}{2}+4\right)=72\)
\(2^{x}\cdot \frac{9}{2}=72\)
\(2^{x}=72:\frac{9}{2}\)
\(2^{x}=16\)
\(2^{x}=2^{4}\)
\(x=4\)Vậy \(x = 4\).

f)

\(\left(2x-\frac{1}{3}\right)^{3}=\frac{-8}{27}\)
\(\left(2x-\frac{1}{3}\right)^{3}=\left(\frac{-2}{3}\right)^{3}\)
\(2x-\frac{1}{3}=\frac{-2}{3}\)
\(2x=\frac{-2}{3}+\frac{1}{3}\)
\(2x=\frac{-1}{3}\)
\(x=\frac{-1}{3}:2\)
\(x=\frac{-1}{6}\)

Vậy \(x = \frac{-1}{6}\).

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