3 ^ (2x) - 2 ^ (x + 1) * 3 ^ x - 3 * 2 ^ (2x) = 0.

log₁.₅3 or 2.70951

Step-by-step explanation:

3^ (2x) - 2^ (x + 1) * 3^x - 3*2^ (2x) = 0 3^ (2x) - 2*2^x*3^x + 2^ (2x) - 4*2^ (2x) = 0 (3^x-2^x) ^2 - (2*2^x) ^2=0 (3^x-2^x+2*2^x) (3^x - 2^x - 2*2^x) = 0 (3^x+2^x) (3^x - 3*2^x) = 0 3^x+2^x>0 for any value of x 3^x - 3*2^x=0 3^x = 3*2^x 3^x/2^x=3 1.5^x=3 x = log₁.₅ 3 = 2.70951