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=31.5^x=3x= log₁.₅ 3 = 2.70951