Question

Solve and check....9^x = 3^x - 2

Answer 1

remember that
logₐx=y means a^y=x
also
if a^n=a^m where a=a, then n=m

try to match bases
remember that 9=3^2
9^x=3^(2x)

3^(2x)=3^(x-2)
2x=x-2
minus x from both sides
x=-2

x=-2

to check

9^-2=3^(-2-2)
1/(9^2)=3^(-4)
1/81=1/(3^4)
1/81=1/81

true

x=-2