What is (log_{a^2}(b))/((log_{sqrt(a))(b^2))} ?

The solution to (log_{a^2}(b))/((log_{sqrt(a))(b^2))} is (log_{a^2}(b))/(2log_{sqrt(a))(b)}

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simplify (log_{a^2}(b))/((log_{sqrt(a))(b^2))}

simplify

\frac{lo g _{a^{2}} ( b )}{( lo g _{a} ( b ^{2} ) )}

\frac{lo g _{a^{2}} ( b )}{2 lo g _{a} ( b )}

Solution steps

\frac{lo g _{a^{2}} ( b )}{lo g _{a} ( b ^{2} )}

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{a} (b^{2}) = 2 lo g_{a} (b)

= \frac{lo g _{a^{2}} ( b )}{2 lo g _{a} ( b )}

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

\frac{\frac{143}{2}}{x} - \frac{1}{4} - \frac{1}{12}

80 - 4 x

4 \frac{( 2 x - 3 )}{3} - 2 \frac{( 3 x + 3 )}{5}

9 x^{2} + 12 x + 4 - 2 (x^{2} - 2 x + 1)

What is (log_{a^2}(b))/((log_{sqrt(a))(b^2))} ?
The solution to (log_{a^2}(b))/((log_{sqrt(a))(b^2))} is (log_{a^2}(b))/(2log_{sqrt(a))(b)}