What is log_{6}(\sqrt[4]{7x}) ?

The solution to log_{6}(\sqrt[4]{7x}) is 1/4 log_{6}(7x)

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simplify log_{6}(\sqrt[4]{7x})

simplify

\frac{1}{4} lo g_{6} (7 x)

Solution steps

Rewrite as

= lo g_{6} ((7 x)^{\frac{1}{4}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{4} lo g_{6} (7 x)

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(7 x^{2} + 5 x + 7) (4 x - 6)

\frac{8 x ^{3} + 12 x ^{2}}{4 x}

What is log_{6}(\sqrt[4]{7x}) ?
The solution to log_{6}(\sqrt[4]{7x}) is 1/4 log_{6}(7x)