Answer:
[tex]x=8[/tex]Step by step explanation:
Solve for x in the following equation:
[tex]\log _x\frac{1}{512}=-3[/tex]We can apply logarithm properties:
[tex]\frac{\ln(\frac{1}{512})}{\ln(x)}=-3[/tex]Multiply both sides by ln(x):
[tex]\begin{gathered} \frac{\ln(\frac{1}{512})}{\ln(x)}\cdot\ln (x)=-3\ln (x) \\ \end{gathered}[/tex]Then, solve for x:
[tex]\begin{gathered} \ln (\frac{1}{512})=-3\ln (x) \\ e^{\ln (\frac{1}{512})}=e^{-3\ln (x)} \\ x=8 \\ \end{gathered}[/tex]