What is log_{10}(((x^3y^{13}))/(z^{13)}) ?

The solution to log_{10}(((x^3y^{13}))/(z^{13)}) is 3log_{10}(x)+13log_{10}(y)-13log_{10}(z)

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simplify log_{10}(((x^3y^{13}))/(z^{13)})

simplify

lo g_{10} (\frac{( x ^{3} y ^{13} )}{z ^{13}})

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

Solution steps

lo g_{10} (\frac{x ^{3} y ^{13}}{z ^{13}})

Apply log rule:

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

lo g_{10} (\frac{x ^{3} y ^{13}}{z ^{13}}) = lo g_{10} (x^{3} y^{13}) - lo g_{10} (z^{13})

= lo g_{10} (x^{3} y^{13}) - lo g_{10} (z^{13})

lo g_{10} (x^{3} y^{13}) = 3 lo g_{10} (x) + 13 lo g_{10} (y)

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

= 3 lo g_{10} (x) + 13 lo g_{10} (y) - 13 lo g_{10} (z)

ln (\frac{325}{310})

lo g_{10} (7 x) \cdot lo g_{10} (4)

lo g_{10} (50 \cdot 5^{\frac{1}{2}}) + 3 lo g_{10} (99)

ln (1 5^{'} 83)

4 lo g_{3} (x) + \frac{1}{3} lo g_{3} (y) - 5 lo g_{3} (z)

What is log_{10}(((x^3y^{13}))/(z^{13)}) ?
The solution to log_{10}(((x^3y^{13}))/(z^{13)}) is 3log_{10}(x)+13log_{10}(y)-13log_{10}(z)