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