Question

The value of x satisfying $lo{g}_2(3x-2)=log{}_{1/2}x$ is

• A. $1$
• B. $-\frac{1}{3}$
• C. $-1$
• D. $\frac{1}{3}$

Answer 1

Answer: (A)

Given, $lo{g}_2(3x-2)=lo{g}_{\frac{1}{2}}x$
$\Rightarrow \frac{log(3x-2)}{log2}=\frac{logx}{log\frac{1}{2}}=\frac{logx}{-log2}$
$\Rightarrow log(3x-2)=log\frac{1}{x}$
$\Rightarrow 3x^2-2x-1=0$
$\Rightarrow (x-1)(x+\frac{1}{3})=0$
$\Rightarrow x=1,x=-\frac{1}{3}$
But $x=-\frac{1}{3}$ is not satisfied in $lo{g}_{\frac{1}{2}}x$.
Hence, $x=1$ is the required solution.