solve the equation

This can be simplified to:

\(3^{-2}=x+2\)

Then, just solve the linear equation:

\(\frac{1}{9}=x+2\\ x=\boxed{-\frac{17}{9}}\)

log₃ (x+2) = - 2

log(x+2) / log 3 = - 2

log(x+2) = - 2 log3

 

 

 

 

log (x+2) = log3^-2

x+2 = 1/3²

x = -2 + 1/9 = - 17/9