What is log_{10}((x^2y^2)/(z^{15)}) ?

The solution to log_{10}((x^2y^2)/(z^{15)}) is 2log_{10}(x)+2log_{10}(y)-15log_{10}(z)

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simplify log_{10}((x^2y^2)/(z^{15)})

simplify

lo g_{10} (\frac{x ^{2} y ^{2}}{z ^{15}})

2 lo g_{10} (x) + 2 lo g_{10} (y) - 15 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x ^{2} y ^{2}}{z ^{15}})

Apply log rule:

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

lo g_{10} (\frac{x ^{2} y ^{2}}{z ^{15}}) = lo g_{10} (x^{2} y^{2}) - lo g_{10} (z^{15})

= lo g_{10} (x^{2} y^{2}) - lo g_{10} (z^{15})

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

lo g_{10} (z^{15}) = 15 lo g_{10} (z)

= 2 lo g_{10} (x) + 2 lo g_{10} (y) - 15 lo g_{10} (z)

3 lo g_{a} (5 x^{2}) - \frac{1}{4} lo g_{a} (8 x + 19)

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

[3 ln (3) - 1 - 2 ln (2)] - [3 ln (3) - 1 - 2 ln (2)]

ln (24) - ln (3)

ln (\frac{e ^{5}}{10})

What is log_{10}((x^2y^2)/(z^{15)}) ?
The solution to log_{10}((x^2y^2)/(z^{15)}) is 2log_{10}(x)+2log_{10}(y)-15log_{10}(z)