Question

Trying to use the app to solve this problem. Please help!!!!
`log_(x) (1)/(512) = - 3`

Answer 1

`x=8`

Step by step explanation:

Solve for x in the following equation:

`\log _x(1)/(512)=-3`

We can apply logarithm properties:

`(\ln((1)/(512)))/(\ln(x))=-3`

Multiply both sides by ln(x):

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

Then, solve for x:

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