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  4. If log 175(5 x)= log 343 7 x, then the value of log 42(x4-2 x2+7) is equal to

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

Continuity and Differentiability

Solution:

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