What is 3log_{b}(y)-7/2 log_{b}(x) ?

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

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simplify 3log_{b}(y)-7/2 log_{b}(x)

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

ln (e^{x}) + ln (- 1)

\frac{1}{2} ln (\frac{39}{59})

lo g_{10} (f (x) (\frac{cos ( x )}{x ^{2} + cos ( x )}))

ln (\frac{1}{5 n + 8}) + ln (7 n + 5)

- lo g_{10} (1.866 \cdot 1 0^{- 10})

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