What is log_{a}((x^2y^3)/(z^4)) ?

The solution to log_{a}((x^2y^3)/(z^4)) is 2log_{a}(x)+3log_{a}(y)-4log_{a}(z)

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simplify log_{a}((x^2y^3)/(z^4))

simplify

lo g_{a} (\frac{x ^{2} y ^{3}}{z ^{4}})

2 lo g_{a} (x) + 3 lo g_{a} (y) - 4 lo g_{a} (z)

Solution steps

lo g_{a} (\frac{x ^{2} y ^{3}}{z ^{4}})

Apply log rule:

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

lo g_{a} (\frac{x ^{2} y ^{3}}{z ^{4}}) = lo g_{a} (x^{2} y^{3}) - lo g_{a} (z^{4})

= lo g_{a} (x^{2} y^{3}) - lo g_{a} (z^{4})

lo g_{a} (x^{2} y^{3}) = 2 lo g_{a} (x) + 3 lo g_{a} (y)

lo g_{a} (z^{4}) = 4 lo g_{a} (z)

= 2 lo g_{a} (x) + 3 lo g_{a} (y) - 4 lo g_{a} (z)

lo g_{6} (a b^{3} c^{2})

lo g_{10} (\frac{x}{y}) + lo g_{10} (\frac{y ^{2}}{x})

ln (4) + ln (8) - ln (16)

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

3 ln (x - 1) + 4 ln (x - 6) - \frac{1}{3} ln (2 x - 1)

What is log_{a}((x^2y^3)/(z^4)) ?
The solution to log_{a}((x^2y^3)/(z^4)) is 2log_{a}(x)+3log_{a}(y)-4log_{a}(z)