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

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