Question

If ${\log }_{175}(5x)={\log }_{343}7x$, then the value of ${\log }_{42}\left(x^4-2x^2+7\right)$ is equal to

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (A)

${\log }_{175}5x={\log }_{343}7x=k$
$\Rightarrow \frac{5}{7}={\left(\frac{175}{343}\right)}^k\Rightarrow k=\frac{1}{2}\Rightarrow x=\sqrt{7}$