What is 4ln(w)-1/5 ln(p) ?

The solution to 4ln(w)-1/5 ln(p) is ln((w^4p^{4/5})/p)

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simplify 4ln(w)-1/5 ln(p)

simplify

4 ln (w) - \frac{1}{5} ln (p)

ln (\frac{w ^{4} p ^{\frac{4}{5}}}{p})

Solution steps

4 ln (w) - \frac{1}{5} ln (p)

Apply log rule:

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

4 ln (w) = ln (w^{4})

= ln (w^{4}) - \frac{1}{5} ln (p)

Apply log rule:

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

\frac{1}{5} ln (p) = ln (p^{\frac{1}{5}})

= ln (w^{4}) - ln (p^{\frac{1}{5}})

Apply log rule:

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

ln (w^{4}) - ln (p^{\frac{1}{5}}) = ln (\frac{w ^{4}}{p ^{\frac{1}{5}}})

= ln (\frac{w ^{4}}{p ^{\frac{1}{5}}})

Simplify

\frac{w ^{4}}{p ^{\frac{1}{5}}} : \frac{w ^{4} p ^{\frac{4}{5}}}{p}

= ln (\frac{w ^{4} p ^{\frac{4}{5}}}{p})

ln (\frac{e ^{2}}{8})

lo g_{3} (u \cdot v \cdot w^{4})

lo g_{6} (x^{8} \frac{y}{z ^{3}})

4 lo g_{10} (5) + 3 lo g_{10} (x)

ln (\frac{2 + x}{2 - x})

What is 4ln(w)-1/5 ln(p) ?
The solution to 4ln(w)-1/5 ln(p) is ln((w^4p^{4/5})/p)