What is 4ln(c)(ln(a)-3ln(b)) ?

The solution to 4ln(c)(ln(a)-3ln(b)) is 4ln(c)ln(a/(b^3))

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simplify 4ln(c)(ln(a)-3ln(b))

simplify

4 ln (c) (ln (a) - 3 ln (b))

4 ln (c) ln (\frac{a}{b ^{3}})

Solution steps

4 ln (c) (ln (a) - 3 ln (b))

Apply log rule:

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

3 ln (b) = ln (b^{3})

= 4 ln (c) (ln (a) - ln (b^{3}))

Apply log rule:

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

ln (a) - ln (b^{3}) = ln (\frac{a}{b ^{3}})

= 4 ln (c) ln (\frac{a}{b ^{3}})

\frac{1}{2} ln (x) + \frac{1}{2} ln (\frac{p x}{p y} x)

ln (\frac{20}{8})

ln (\frac{1}{\frac{95}{100}})

ln (\frac{1}{w})

ln (\frac{\frac{1}{2} x}{x})

What is 4ln(c)(ln(a)-3ln(b)) ?
The solution to 4ln(c)(ln(a)-3ln(b)) is 4ln(c)ln(a/(b^3))