Question

equação exponencial 8^2x x 9^3x = 216

Answer 1

Resposta:

x=1/2

Explicação passo-a-passo:

$\displaystyle8^{2x}.9^{3x}=216\\8|2\\4|2\\2|2\\1|1\\ 8=2.2.2=2^{3}\\\\9|3\\3|3\\1|1\\ 9=3.3=3^{2}\\\\216|2\\108|2\\54|2\\27|3\\9|3\\3|3\\1|1\\216=2.2.2.3.3.3=2^{3}.3^{3}\\\\2^{3(2x)}.3^{2(3x)}=2^{3}.3^{3}\\2^{6x}.3^{6x}=2^{3}.3^{3}\\6x=3\\x=\frac{3\div3}{6\div3}=\frac{1}{2}$