What is log_{c}((x^{1/2}y^3)/(x^4)) ?

The solution to log_{c}((x^{1/2}y^3)/(x^4)) is 3log_{c}(y)-7/2 log_{c}(x)

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simplify log_{c}((x^{1/2}y^3)/(x^4))

simplify

lo g_{c} (\frac{x ^{\frac{1}{2}} y ^{3}}{x ^{4}})

3 lo g_{c} (y) - \frac{7}{2} lo g_{c} (x)

Solution steps

lo g_{c} (\frac{x ^{\frac{1}{2}} y ^{3}}{x ^{4}})

Simplify

\frac{x ^{\frac{1}{2}}}{x ^{4}} : \frac{1}{x ^{\frac{7}{2}}}

= lo g_{c} (\frac{y ^{3}}{x ^{\frac{7}{2}}})

Apply log rule:

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

lo g_{c} (\frac{y ^{3}}{x ^{\frac{7}{2}}}) = lo g_{c} (y^{3}) - lo g_{c} (x^{\frac{7}{2}})

= lo g_{c} (y^{3}) - lo g_{c} (x^{\frac{7}{2}})

lo g_{c} (y^{3}) = 3 lo g_{c} (y)

lo g_{c} (x^{\frac{7}{2}}) = \frac{7}{2} lo g_{c} (x)

= 3 lo g_{c} (y) - \frac{7}{2} lo g_{c} (x)

\frac{1}{4} lo g_{b} (x) + 3 lo g_{b} (y) - 5 lo g_{b} (x)

2 ln (x) - \frac{1}{3} ln (y) + 4 ln (z)

lo g_{2} (x^{3} y^{2})

lo g_{10} ((\frac{m}{n}) \cdot (\frac{p}{q}))

lo g_{2} (\frac{a ^{2} - 9}{5})

What is log_{c}((x^{1/2}y^3)/(x^4)) ?
The solution to log_{c}((x^{1/2}y^3)/(x^4)) is 3log_{c}(y)-7/2 log_{c}(x)