Question

If $8^{x+1}–8^x–8^{x–1}=880$, then the value of x is equal to

• A. $\frac{5}{2}$
• B. $\frac{9}{5}$
• C. 2
• D. $\frac{7}{3}$

Answer 1

The correct option is D $\frac{7}{3}$

$8^{x+1}–8^x–8^{x–1}=880$
Let $8^x=t$
$\Rightarrow 8^x{.8}^1-8^x-8^x{.8}^{-1}=880$
$\Rightarrow 8t-t-\frac{t}{8}=880$
$\Rightarrow 7t-\frac{t}{8}=880$
$\Rightarrow \frac{55t}{8}=880$
$\Rightarrow t=\frac{880\times 8}{55}$
$\Rightarrow t=\frac{80\times 8}{5}=16\times 8=128$
$\Rightarrow 8^x=128$ $(\because 8^x=t)$
$\Rightarrow 2^{3x}=2^7$
$\Rightarrow 3x=7$
$\Rightarrow x=\frac{7}{3}$
Hence, the correct answer is option (d).