Question

2^x-1+5.2^x-2=7/32

Answer 1

\(2^{\left(x-1\right)}+5.2^{\left(x-2\right)}=\frac{7}{32}\)

\(\Leftrightarrow2.2^{x-2}+5.2^{x-2}=\frac{7}{32}\)

\(\Leftrightarrow\left(2+5\right).2^{x-2}=\frac{7}{32}\)

\(\Leftrightarrow7.2^{x-2}=\frac{7}{32}\)

\(\Leftrightarrow2^{x-2}=\frac{7}{32}:7\)

\(\Leftrightarrow2^{x-2}=\frac{1}{32}=2^{-5}\)

\(\Leftrightarrow x-2=-5\)

\(\Leftrightarrow x=\left(-5\right)+2\)

\(\Leftrightarrow x=-3\)

Vậy \(x=-3\).

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