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

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

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

simplify

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

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

Solution steps

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

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

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

lo g_{10} (x^{3}) = 3 lo g_{10} (x)

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

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

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

3 ln (x) - 2 ln (y)

3 ln (x) + 5 ln (y) - 2 ln (z)

ln (\frac{e x ^{2}}{x + 1})

ln (x) + ln (x + 1)

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