What is 1/((log_{x)(xy))+log_{xy}(y)} ?

The solution to 1/((log_{x)(xy))+log_{xy}(y)} is 1/(1+log_{x)(y)+log_{xy}(y)}

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simplify 1/((log_{x)(xy))+log_{xy}(y)}

simplify

\frac{1}{( lo g _{x} ( x y ) ) + lo g _{x y} ( y )}

\frac{1}{1 + lo g _{x} ( y ) + lo g _{x y} ( y )}

Solution steps

\frac{1}{( lo g _{x} ( x y ) ) + lo g _{x y} ( y )}

Apply rule:

(a) = a

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

= \frac{1}{lo g _{x} ( x y ) + lo g _{x y} ( y )}

Simplify

lo g_{x} (x y) : 1 + lo g_{x} (y)

= \frac{1}{1 + lo g _{x} ( y ) + lo g _{x y} ( y )}

1 + sec^{2} (x) sin^{2} (x)

27 y^{3} + 125 z^{3}

(x^{2})^{- 6}

6 x^{2} - 31 x y + 18 y^{2}

2 (3^{a}) + (3^{a})

What is 1/((log_{x)(xy))+log_{xy}(y)} ?
The solution to 1/((log_{x)(xy))+log_{xy}(y)} is 1/(1+log_{x)(y)+log_{xy}(y)}