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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{10} (x^{13} y^{19}) = 13 lo g_{10} (x) + 19 lo g_{10} (y)

lo g_{10} (z^{13}) = 13 lo g_{10} (z)

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

ln (\frac{( 3 ^{x} 6 ^{3 x} )}{2 ^{3 x}})

lo g_{x} (\frac{1}{4})

192 ln (\frac{s}{762}) - s + 763

lo g_{10} (75 x^{2})

lo g_{3} (x) + lo g_{3} (6 x) - lo g_{3} (x^{2})

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