Question

Solve the equation.logv6 36^x = -2(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

Answer 1

-1

Explanation:

We have the following equation:

`\log _6\mleft(36^x\mright)=-2`

Being a logarithmic equation, we will apply properties of logarithms to solve, like this:

`\begin{gathered} 36^x=u \\ \text{ therefore:} \\ \log _6(u)=-2 \\ u=6^(-2) \\ u=(1)/(6^2)=(1)/(36) \\ \text{ replacing} \\ 36^x=(1)/(36) \\ 36^x=36^(-1) \\ x=-1 \end{gathered}`

The solution set is -1