# Determine (8x)x, if 9x+2 = 240 + 9x.

Question:

Determine $(8 x)^{x}$, if $9^{x+2}=240+9^{x}$.

Solution:

$9^{x+2}=240+9^{x}$

$9^{x} \cdot 9^{2}=240+9^{x}$

Let $9^{x}$ be $y$

81y = 240 + y

81y - y = 240

80y = 240

y = 3

Since, y = 3

Then,

$9^{x}=3$

$3^{2 x}=3$

Therefore, $x=1 / 2$

$(8 x)^{x}=(8 \times 1 / 2)^{1 / 2}$

$=(4)^{1 / 2}$

$=2$

Therefore $(8 x)^{x}=2$