What is log_{10}((x^2)/(y^5)) ?

The solution to log_{10}((x^2)/(y^5)) is 2log_{10}(x)-5log_{10}(y)

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simplify log_{10}((x^2)/(y^5))

simplify

lo g_{10} (\frac{x ^{2}}{y ^{5}})

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

Solution steps

lo g_{10} (\frac{x ^{2}}{y ^{5}})

Apply log rule:

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

lo g_{10} (\frac{x ^{2}}{y ^{5}}) = lo g_{10} (x^{2}) - lo g_{10} (y^{5})

= lo g_{10} (x^{2}) - lo g_{10} (y^{5})

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

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

= 2 lo g_{10} (x) - 5 lo g_{10} (y)

2 ln (x) + 4 ln (y) - 3 ln (z)

ln (x) + ln (3)

lo g_{3} (21) + lo g_{3} (10)

6 ln (x) - 4 ln (y)

(x - y ln (y) + y ln (x)) d x + x (ln (y) - ln (x)) d y

What is log_{10}((x^2)/(y^5)) ?
The solution to log_{10}((x^2)/(y^5)) is 2log_{10}(x)-5log_{10}(y)