What is expand (log_{3}(a^2b))/(log_{3)(z^3)} ?

The solution to expand (log_{3}(a^2b))/(log_{3)(z^3)} is (log_{z}(a^2b))/3

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expand (log_{3}(a^2b))/(log_{3)(z^3)}

expand

\frac{lo g _{3} ( a ^{2} b )}{lo g _{3} ( z ^{3} )}

\frac{lo g _{z} ( a ^{2} b )}{3}

Solution steps

\frac{lo g _{3} ( a ^{2} b )}{lo g _{3} ( z ^{3} )}

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{3} (z^{3}) = 3 lo g_{3} (z)

= \frac{lo g _{3} ( a ^{2} b )}{3 lo g _{3} ( z )}

Apply log rule:

\frac{lo g _{c} ( b )}{lo g _{c} ( a )} = lo g_{a} (b)

\frac{lo g _{3} ( a ^{2} b )}{lo g _{3} ( z )} = lo g_{z} (a^{2} b)

= \frac{lo g _{z} ( a ^{2} b )}{3}

50 ln (10) - 50 ln (5) - 25

lo g_{3} (x y^{2})

30 - 12 ln (x) - 18 ln (y)

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

ln ∣ z + 4 ∣ + 6 (\frac{1}{5} ln ∣ z - 1 ∣ - \frac{1}{5} ln ∣ z + 4 ∣)

What is expand (log_{3}(a^2b))/(log_{3)(z^3)} ?
The solution to expand (log_{3}(a^2b))/(log_{3)(z^3)} is (log_{z}(a^2b))/3