What is log_{6}((x/(216))^4) ?

The solution to log_{6}((x/(216))^4) is 4log_{6}(x)-12

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simplify log_{6}((x/(216))^4)

simplify

lo g_{6} ((\frac{x}{216})^{4})

4 lo g_{6} (x) - 12

Solution steps

lo g_{6} ((\frac{x}{216})^{4})

Apply log rule

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

lo g_{6} ((\frac{x}{216})^{4}) = 4 lo g_{6} (\frac{x}{216})

= 4 lo g_{6} (\frac{x}{216})

Simplify

lo g_{6} (\frac{x}{216}) : lo g_{6} (x) - 3

= 4 (lo g_{6} (x) - 3)

Expand

4 (lo g_{6} (x) - 3) : 4 lo g_{6} (x) - 12

= 4 lo g_{6} (x) - 12

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What is log_{6}((x/(216))^4) ?
The solution to log_{6}((x/(216))^4) is 4log_{6}(x)-12