What is log_{6}(36x^3) ?

The solution to log_{6}(36x^3) is 2+3log_{6}(x)

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simplify log_{6}(36x^3)

simplify

lo g_{6} (36 x^{3})

2 + 3 lo g_{6} (x)

Solution steps

lo g_{6} (36 x^{3})

Factor the number:

36 = 6^{2}

= lo g_{6} (6^{2} x^{3})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{6} (6^{2} x^{3}) = lo g_{6} (6^{2}) + lo g_{6} (x^{3})

= lo g_{6} (6^{2}) + lo g_{6} (x^{3})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{6} (6^{2}) = 2

= 2 + lo g_{6} (x^{3})

Apply log rule

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

lo g_{6} (x^{3}) = 3 lo g_{6} (x)

= 2 + 3 lo g_{6} (x)

lo g_{10} (x^{\frac{1}{2}} y^{\frac{1}{3}})

- lo g_{10} (6.2 \cdot 1 0^{- 8})

ln (a e^{b x})

\frac{1}{3} ln \frac{3 ( e ^{x^{3}} ) ^{3}}{x ^{6}}

lo g_{10} (\frac{85347 \times 15274}{125386})