What is log_{9}((sqrt(9x^5))/y) ?

The solution to log_{9}((sqrt(9x^5))/y) is (1+2log_{3}(x)+log_{3}(sqrt(x)))/2-log_{9}(y)

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simplify log_{9}((sqrt(9x^5))/y)

simplify

lo g_{9} (\frac{9 x ^{5}}{y})

\frac{1 + 2 lo g _{3} ( x ) + lo g _{3} ( x )}{2} - lo g_{9} (y)

Solution steps

lo g_{9} (\frac{9 x ^{5}}{y})

Simplify

9 x^{5} : 3 x^{2} x

= lo g_{9} (\frac{3 x ^{2} x}{y})

Apply log rule:

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

lo g_{9} (\frac{3 x ^{2} x}{y}) = lo g_{9} (3 x^{2} x) - lo g_{9} (y)

= lo g_{9} (3 x^{2} x) - lo g_{9} (y)

Simplify

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

= \frac{1 + 2 lo g _{3} ( x ) + lo g _{3} ( x )}{2} - lo g_{9} (y)

lo g_{6} (x) - lo g_{6} (x^{4})

4 lo g_{8} (3) - lo g_{8} (6)

lo g_{5} (x^{2}) - lo g_{5} (x)

lo g_{10} (\frac{1}{b})

What is log_{9}((sqrt(9x^5))/y) ?
The solution to log_{9}((sqrt(9x^5))/y) is (1+2log_{3}(x)+log_{3}(sqrt(x)))/2-log_{9}(y)