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Sagot :

The correct answer is:

[tex]-\frac{7}{2}[/tex]

To solve this, we can apply logarithm:

[tex]N=a^x\Leftrightarrow\log _aN=x[/tex]

Then we have:

[tex]\begin{gathered} (\frac{1}{4})^{x+1}=32\Leftrightarrow\log _{\frac{1}{4}}32=x+1 \\ \end{gathered}[/tex]

Then we can solve:

[tex]\begin{gathered} \log _{\frac{1}{4}}32=-\frac{5}{2}\Rightarrow-\frac{5}{2}=x+1 \\ \\ x=-\frac{5}{2}-1=-\frac{7}{2} \end{gathered}[/tex]

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