What is log_{10}((x^3y^2)/(z^4)) ?

The solution to log_{10}((x^3y^2)/(z^4)) is 3log_{10}(x)+2log_{10}(y)-4log_{10}(z)

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simplify log_{10}((x^3y^2)/(z^4))

simplify

lo g_{10} (\frac{x ^{3} y ^{2}}{z ^{4}})

3 lo g_{10} (x) + 2 lo g_{10} (y) - 4 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x ^{3} y ^{2}}{z ^{4}})

Apply log rule:

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

lo g_{10} (\frac{x ^{3} y ^{2}}{z ^{4}}) = lo g_{10} (x^{3} y^{2}) - lo g_{10} (z^{4})

= lo g_{10} (x^{3} y^{2}) - lo g_{10} (z^{4})

lo g_{10} (x^{3} y^{2}) = 3 lo g_{10} (x) + 2 lo g_{10} (y)

lo g_{10} (z^{4}) = 4 lo g_{10} (z)

= 3 lo g_{10} (x) + 2 lo g_{10} (y) - 4 lo g_{10} (z)

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

2 lo g_{2} (x) + 3 lo g_{2} (y)

ln (x^{2} - 1) - ln (x + 1)

\frac{7}{4} ln (x) - \frac{5}{4} ln (y) - \frac{1}{4} ln (z) + \frac{1}{4} ln (x)

ln (\frac{2}{e})

What is log_{10}((x^3y^2)/(z^4)) ?
The solution to log_{10}((x^3y^2)/(z^4)) is 3log_{10}(x)+2log_{10}(y)-4log_{10}(z)