Question

solve for x.
$5 + \log_{2}(-5x) = 9$

Explanation:

Step1: Isolate the logarithmic term

Subtract 5 from both sides of the equation \(5 + \log_{2}(-5x)=9\) to get \(\log_{2}(-5x)=9 - 5\).
\(\log_{2}(-5x)=4\)

Step2: Convert logarithmic equation to exponential form

Recall that if \(\log_{a}b = c\), then \(a^{c}=b\). For \(\log_{2}(-5x)=4\), we have \(2^{4}=-5x\).
\(16=-5x\)

Step3: Solve for x

Divide both sides of the equation \(16 = - 5x\) by \(-5\) to isolate \(x\).
\(x=\frac{16}{-5}=-\frac{16}{5}\)

Answer:

\(-\frac{16}{5}\)