What is log_{b}((a^{(-3)/2})/(b^4)) ?

The solution to log_{b}((a^{(-3)/2})/(b^4)) is -3/2 log_{b}(a)-4

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simplify log_{b}((a^{(-3)/2})/(b^4))

simplify

lo g_{b} (\frac{a ^{\frac{- 3}{2}}}{b ^{4}})

- \frac{3}{2} lo g_{b} (a) - 4

Solution steps

lo g_{b} (\frac{a ^{\frac{- 3}{2}}}{b ^{4}})

Apply log rule:

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

lo g_{b} (\frac{a ^{\frac{- 3}{2}}}{b ^{4}}) = lo g_{b} (a^{\frac{- 3}{2}}) - lo g_{b} (b^{4})

= lo g_{b} (a^{\frac{- 3}{2}}) - lo g_{b} (b^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{b} (a^{\frac{- 3}{2}}) = \frac{- 3}{2} lo g_{b} (a)

= \frac{- 3}{2} lo g_{b} (a) - lo g_{b} (b^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{b} (b^{4}) = 4 lo g_{b} (b)

= \frac{- 3}{2} lo g_{b} (a) - 4 lo g_{b} (b)

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{3}{2} lo g_{b} (a) - 4 lo g_{b} (b)

4 lo g_{b} (b) = 4

= - \frac{3}{2} lo g_{b} (a) - 4

ln (a^{5})

- ln (- 6 e^{x})

- 0.25 ln (1.33813 2. 5^{2} + 0.55848)

ln (\frac{2.01}{1.7})

4.8 + lo g_{10} (\frac{( 0.008 )}{( 0.012 )})

What is log_{b}((a^{(-3)/2})/(b^4)) ?
The solution to log_{b}((a^{(-3)/2})/(b^4)) is -3/2 log_{b}(a)-4