Question

o valor de x é? (foto acima)​

Answer 1

Resposta:

x=11/12

Explicação passo-a-passo:

$2.2^x=\sqrt{8}.\sqrt[4]{2}.\sqrt[6]{2} \\\\2^{(1+x)}=\sqrt{2^3}.2^{\frac{1}{4}}.2^{\frac{1}{6}}\\\\2^{(1+x)}=2^{\frac{3}{2} }.2^{\frac{1}{4}}.2^{\frac{1}{6}}\\\\2^{(1+x)}=2^{(\frac{3}{2}+\frac{1}{4}+\frac{1}{6})}}\\\\1+x=\frac{3}{2}+\frac{1}{4}+\frac{1}{6}$

mmc (3,4,6)

3,4,6|2

3,2,3|2

3,1,3|3

1,1,1

mmc (3,4,6) = 2.2.3=12

$\frac{12(1+x)}{12} =\frac{18+3+2}{12} \\\\12+12x=23\\12x=23-12\\12x=11\\x=\frac{11}{12}$