What is log_{5}((x^3)/(y^2)) ?

The solution to log_{5}((x^3)/(y^2)) is 3log_{5}(x)-2log_{5}(y)

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simplify log_{5}((x^3)/(y^2))

simplify

lo g_{5} (\frac{x ^{3}}{y ^{2}})

3 lo g_{5} (x) - 2 lo g_{5} (y)

Solution steps

lo g_{5} (\frac{x ^{3}}{y ^{2}})

Apply log rule:

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

lo g_{5} (\frac{x ^{3}}{y ^{2}}) = lo g_{5} (x^{3}) - lo g_{5} (y^{2})

= lo g_{5} (x^{3}) - lo g_{5} (y^{2})

lo g_{5} (x^{3}) = 3 lo g_{5} (x)

lo g_{5} (y^{2}) = 2 lo g_{5} (y)

= 3 lo g_{5} (x) - 2 lo g_{5} (y)

2 ln (15) + ln (5)

- \frac{1}{14} lo g_{2} (\frac{1210689028125}{1 4 ^{14}})

ln (3 x + 2) + ln (x + 4)

ln (\frac{x ^{3} x - 1}{3 x + 4})

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

What is log_{5}((x^3)/(y^2)) ?
The solution to log_{5}((x^3)/(y^2)) is 3log_{5}(x)-2log_{5}(y)