What is log_{9}((sqrt(9x^7))/y) ?

The solution to log_{9}((sqrt(9x^7))/y) is (1+6log_{9}(x)+log_{3}(sqrt(x)))/2-log_{9}(y)

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simplify log_{9}((sqrt(9x^7))/y)

simplify

lo g_{9} (\frac{9 x ^{7}}{y})

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

Solution steps

lo g_{9} (\frac{9 x ^{7}}{y})

Simplify

9 x^{7} : 3 x^{3} x

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

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

Simplify

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

= \frac{1 + 6 lo g _{9} ( x ) + lo g _{3} ( x )}{2} - lo g_{9} (y)

5 lo g_{10} (x) + 3 lo g_{10} (x^{2})

ln (9 x (2 x + 5))

2 (lo g_{7} (x) + 2 lo g_{7} (y) - 4 lo g_{7} (z))

\frac{1}{8} ln (3) - \frac{1}{8} ln (8)

lo g_{5} (3) - lo g_{5} (t)

What is log_{9}((sqrt(9x^7))/y) ?
The solution to log_{9}((sqrt(9x^7))/y) is (1+6log_{9}(x)+log_{3}(sqrt(x)))/2-log_{9}(y)