Question

Utilize as propriedades de potência e encontre o valor de x nessa equação exponencial :

3^2x-2 . 9^x+1 = 27^2-x

Answer 1

$3^{2x-2}.9^{x+1}=27^{2-x}\\\\ 3^{2x-2}.(3^2)^{x+1}=(3^3)^{2-x}\\\\ 3^{2x-2}.3^{2x+2}=3^{6-3x}\\\\ 3^{2x-2+2x+2}=3^{6-3x}\\\\ 3^{4x}=3^{6-3x}\\\\ 4x=6-3x\\\\ 4x+3x=6\\\\ 7x=6\\\\ x=\frac{6}{7}$