Solve $8^{x+1} = 32 \cdot\sqrt2$ without $\log$ I need help solving the equation $8^{x+1} = 32 \cdot\sqrt2$. The obvious answer is to use log, but that is reserved for the next section. The example given for this section of questions is:
$4^x = 8$
$(2^2)^x = 2^3$
$2x = 3$
$x = \dfrac{3}{2}$
The example looks obvious and easy to solve, but I do not understand where you'd use this for my question.

$$
8^{x+1} = 32 \sqrt{2} 
$$
$$
8\times 8^x = 32 \sqrt{2}
$$
$$
8^x =2^{3x}= 4\sqrt{2}=2^2\times 2^{1/2}= 2^{2,5}
$$
$$
3x=2,5 \to x=\frac{5}{6}
$$
