What is log_{10}((x^{15}y^{13})/(z^{19)}) ?

The solution to log_{10}((x^{15}y^{13})/(z^{19)}) is 15log_{10}(x)+13log_{10}(y)-19log_{10}(z)

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simplify log_{10}((x^{15}y^{13})/(z^{19)})

simplify

lo g_{10} (\frac{x ^{15} y ^{13}}{z ^{19}})

15 lo g_{10} (x) + 13 lo g_{10} (y) - 19 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x ^{15} y ^{13}}{z ^{19}})

Apply log rule:

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

lo g_{10} (\frac{x ^{15} y ^{13}}{z ^{19}}) = lo g_{10} (x^{15} y^{13}) - lo g_{10} (z^{19})

= lo g_{10} (x^{15} y^{13}) - lo g_{10} (z^{19})

lo g_{10} (x^{15} y^{13}) = 15 lo g_{10} (x) + 13 lo g_{10} (y)

lo g_{10} (z^{19}) = 19 lo g_{10} (z)

= 15 lo g_{10} (x) + 13 lo g_{10} (y) - 19 lo g_{10} (z)

2 ln (x) - 4 ln (y)

\frac{1}{3} ln (y) + ln (z)

lo g_{4} (x^{2} - 64) - 5 lo g_{4} (x + 8)

lo g_{10} (6) - 3 lo g_{10} (\frac{1}{3})

What is log_{10}((x^{15}y^{13})/(z^{19)}) ?
The solution to log_{10}((x^{15}y^{13})/(z^{19)}) is 15log_{10}(x)+13log_{10}(y)-19log_{10}(z)