Question

If ${32}^{x-2}=2^{6-3x}$, then the value of $x$ is:

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{8}$
• D. $2$

Answer 1

Answer: (D)

$2$

Consider ${32}^{x-2}=2^{6-3x}$and simplify it as follows:

${32}^{x-2}=2^{6-3x}\Rightarrow {32}^x\times {32}^{-2}=2^6\times 2^{-3x}\Rightarrow {\left({\left(2\right)}^5\right)}^x\times {\left({\left(2\right)}^5\right)}^{-2}=2^6\times 2^{-3x}\Rightarrow 2^{5x}\times 2^{-10}=2^6\times 2^{-3x}\Rightarrow 2^{5x}\times 2^{3x}=2^6\times 2^{10}\Rightarrow 2^{5x+3x}=2^{6+10}\Rightarrow 2^{8x}=2^{16}\Rightarrow 8x=16\Rightarrow x=2$

Hence, $x=2$.