Question

If $\frac{lo{g}_2(9-2^x)}{3-x}=1$, then value of x is

• A. x = 4
• B. x = + 1 or -1
• C. x = $\pm$ 2
• D. x = 0

Answer 1

The correct option is D x = 0

We have,

$\frac{lo{g}_2(9-2^x)}{3-x}=1$

$lo{g}_2(9-2^x)=3-x$

$9-2^x=2^{3-x}$ $..........\left(1\right)$

From option $\left(D\right)$

$9-2^0=2^{3-0}$

$9-1=2^3$

$8=8$

Hence, $x=0$ is the root of this equation.

Hence, only option $D$ is correct.