What is log_{4}((c^{1/8})/(c^8)) ?

The solution to log_{4}((c^{1/8})/(c^8)) is -(63log_{4}(c))/8

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simplify log_{4}((c^{1/8})/(c^8))

simplify

lo g_{4} (\frac{c ^{\frac{1}{8}}}{c ^{8}})

- \frac{63 lo g _{4} ( c )}{8}

Solution steps

lo g_{4} (\frac{c ^{\frac{1}{8}}}{c ^{8}})

Simplify

\frac{c ^{\frac{1}{8}}}{c ^{8}} : \frac{1}{c ^{\frac{63}{8}}}

= lo g_{4} (\frac{1}{c ^{\frac{63}{8}}})

Simplify

\frac{1}{c ^{\frac{63}{8}}} : (c^{\frac{63}{8}})^{- 1}

= lo g_{4} ((c^{\frac{63}{8}})^{- 1})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{4} ((c^{\frac{63}{8}})^{- 1}) = - 1 \cdot lo g_{4} (c^{\frac{63}{8}})

= - 1 \cdot lo g_{4} (c^{\frac{63}{8}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{4} (c^{\frac{63}{8}}) = \frac{63}{8} lo g_{4} (c)

= - 1 \cdot \frac{63}{8} lo g_{4} (c)

Simplify

- 1 \cdot \frac{63}{8} lo g_{4} (c) : - \frac{63 lo g _{4} ( c )}{8}

= - \frac{63 lo g _{4} ( c )}{8}

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What is log_{4}((c^{1/8})/(c^8)) ?
The solution to log_{4}((c^{1/8})/(c^8)) is -(63log_{4}(c))/8