What is log_{9}((3x^3)/y) ?

The solution to log_{9}((3x^3)/y) is (6log_{9}(x)+1)/2-log_{9}(y)

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simplify log_{9}((3x^3)/y)

simplify

lo g_{9} (\frac{3 x ^{3}}{y})

\frac{6 lo g _{9} ( x ) + 1}{2} - lo g_{9} (y)

Solution steps

lo g_{9} (\frac{3 x ^{3}}{y})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{9} (\frac{3 x ^{3}}{y}) = lo g_{9} (3 x^{3}) - lo g_{9} (y)

= lo g_{9} (3 x^{3}) - lo g_{9} (y)

Simplify

lo g_{9} (3 x^{3}) : \frac{6 lo g _{9} ( x ) + 1}{2}

= \frac{6 lo g _{9} ( x ) + 1}{2} - lo g_{9} (y)

lo g_{n} (\frac{4}{n})

\frac{2}{3} lo g_{10} (7)

lo g_{b} (\frac{p ^{3} q ^{6}}{m ^{5} b ^{7}})

7 lo g_{b} (x) + 5 lo g_{b} (z)

lo g_{a} (\frac{1}{2})

What is log_{9}((3x^3)/y) ?
The solution to log_{9}((3x^3)/y) is (6log_{9}(x)+1)/2-log_{9}(y)