Question

If $\log x^2-\log 2x=3\log 3-\log 6$, then $x$ is equal to

• A. $9$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is A $9$

$\log x^2-\log 2x=3\log 3-\log 6$, where, $x>0$
$\log x^2=2\log x[\because \log a^m=m\log a]\to$ (1)
$\log 2x=\log 2+\log x[\because \log (ab)=\log a+\log b]\to$ (2)
Using (1) and (2)
$\Rightarrow 2\log x-\log 2-\log x=3\log 3-\log 2-\log 3$
$\Rightarrow \log x=2\log 3$
$\Rightarrow x=9$
Ans: A