What is log_{10}((x^3)/(y^5)) ?

The solution to log_{10}((x^3)/(y^5)) is 3log_{10}(x)-5log_{10}(y)

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simplify log_{10}((x^3)/(y^5))

simplify

lo g_{10} (\frac{x ^{3}}{y ^{5}})

3 lo g_{10} (x) - 5 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x ^{3}}{y ^{5}})

Apply log rule:

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

lo g_{10} (\frac{x ^{3}}{y ^{5}}) = lo g_{10} (x^{3}) - lo g_{10} (y^{5})

= lo g_{10} (x^{3}) - lo g_{10} (y^{5})

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

lo g_{10} (y^{5}) = 5 lo g_{10} (y)

= 3 lo g_{10} (x) - 5 lo g_{10} (y)

lo g_{10} (\frac{u ^{4}}{v})

6 lo g_{3} (x) + 2 lo g_{3} (11)

lo g_{4} (\frac{\frac{x}{z}}{w})

lo g_{10} (20) + lo g_{10} (15) - 2 lo g_{10} (5)

\frac{3}{2} lo g_{10} (a) + \frac{5}{2} lo g_{10} (b)

What is log_{10}((x^3)/(y^5)) ?
The solution to log_{10}((x^3)/(y^5)) is 3log_{10}(x)-5log_{10}(y)