What is expand log_{3}(12^{5/6})x^9 ?

The solution to expand log_{3}(12^{5/6})x^9 is (5log_{3}(12)x^9)/6

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expand log_{3}(12^{5/6})x^9

expand

lo g_{3} (1 2^{\frac{5}{6}}) x^{9}

\frac{5 lo g _{3} ( 12 ) x ^{9}}{6}

Solution steps

lo g_{3} (1 2^{\frac{5}{6}}) x^{9}

Apply log rule:

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

lo g_{3} (1 2^{\frac{5}{6}}) = \frac{5}{6} lo g_{3} (12)

= \frac{5}{6} lo g_{3} (12) x^{9}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= lo g_{3} (12) \frac{5 x ^{9}}{6}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 x ^{9} lo g _{3} ( 12 )}{6}

lo g_{5} (\frac{x}{125})

ln (\frac{e ^{5}}{4})

ln (ln (y)) + ln (y)

ln (\frac{( 3 ^{x} 6 ^{3 x} )}{2 ^{4 x}})

lo g_{10} (x) + lo g_{10} (y) + lo g_{10} (z)

What is expand log_{3}(12^{5/6})x^9 ?
The solution to expand log_{3}(12^{5/6})x^9 is (5log_{3}(12)x^9)/6