Answer
$x\approx-1.98$
Work Step by Step
Use the definition of the log function to solve for $x$. Rewrite the problem so that the base has the exponent of the opposite side and is equal to the log's number and/or variable.
$\log_7(x+2)=-2$
$7^{-2}=x+2$
$7^{-2}-2=x$
$\frac{1}{49}-\frac{98}{49}=x$
$x\approx-1.98$
