What is log_{a}((x^{1/2}y^5)/(x^3)) ?

The solution to log_{a}((x^{1/2}y^5)/(x^3)) is 5log_{a}(y)-5/2 log_{a}(x)

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simplify log_{a}((x^{1/2}y^5)/(x^3))

simplify

lo g_{a} (\frac{x ^{\frac{1}{2}} y ^{5}}{x ^{3}})

5 lo g_{a} (y) - \frac{5}{2} lo g_{a} (x)

Solution steps

lo g_{a} (\frac{x ^{\frac{1}{2}} y ^{5}}{x ^{3}})

Simplify

\frac{x ^{\frac{1}{2}}}{x ^{3}} : \frac{1}{x ^{\frac{5}{2}}}

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

Apply log rule:

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

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

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

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

lo g_{a} (x^{\frac{5}{2}}) = \frac{5}{2} lo g_{a} (x)

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

lo g_{10} (\frac{p ^{6}}{q ^{1}})

lo g_{10} (12 x^{2})

20 lo g_{10} (\frac{4 π}{\frac{1}{8}}) - 20 lo g_{10} (0.5)

- (\frac{3}{8} lo g_{2} (\frac{3}{8}) + \frac{5}{8} lo g_{2} (\frac{5}{8}))

5 lo g_{7} (2 x) - \frac{1}{3} lo g_{7} (5 x - 1)

What is log_{a}((x^{1/2}y^5)/(x^3)) ?
The solution to log_{a}((x^{1/2}y^5)/(x^3)) is 5log_{a}(y)-5/2 log_{a}(x)