Question

Trying to use the app to solve this problem. Please help!!!! $log_{x} \frac{1}{512} = - 3$

Answer 1

Answer:

$x=8$

Step by step explanation:

Solve for x in the following equation:

$\log _x\frac{1}{512}=-3$

We can apply logarithm properties:

$\frac{\ln(\frac{1}{512})}{\ln(x)}=-3$

Multiply both sides by ln(x):

$\begin{gathered} \frac{\ln(\frac{1}{512})}{\ln(x)}\cdot\ln (x)=-3\ln (x) \\ \end{gathered}$

Then, solve for x:

$\begin{gathered} \ln (\frac{1}{512})=-3\ln (x) \\ e^{\ln (\frac{1}{512})}=e^{-3\ln (x)} \\ x=8 \\ \end{gathered}$