What is 6/5 ln|z-1|-6/5 ln|z+4| ?

The solution to 6/5 ln|z-1|-6/5 ln|z+4| is ln(\sqrt[5]{((z-1)^6)/((z+4)^6)})

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simplify 6/5 ln|z-1|-6/5 ln|z+4|

simplify

\frac{6}{5} ln ∣ z - 1 ∣ - \frac{6}{5} ln ∣ z + 4 ∣

Solution steps

\frac{6}{5} ln ∣ z - 1 ∣ - \frac{6}{5} ln ∣ z + 4 ∣

Apply log rule:

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

\frac{6}{5} ln ∣ z - 1 ∣ = ln (∣ z - 1 ∣^{\frac{6}{5}})

= ln (∣ z - 1 ∣^{\frac{6}{5}}) - \frac{6}{5} ln ∣ z + 4 ∣

Apply log rule:

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

\frac{6}{5} ln ∣ z + 4 ∣ = ln (∣ z + 4 ∣^{\frac{6}{5}})

= ln (∣ z - 1 ∣^{\frac{6}{5}}) - ln (∣ z + 4 ∣^{\frac{6}{5}})

Apply log rule:

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

ln (∣ z - 1 ∣^{\frac{6}{5}}) - ln (∣ z + 4 ∣^{\frac{6}{5}}) = ln (\frac{∣ z - 1 ∣ ^{\frac{6}{5}}}{∣ z + 4 ∣ ^{\frac{6}{5}}})

= ln (\frac{∣ z - 1 ∣ ^{\frac{6}{5}}}{∣ z + 4 ∣ ^{\frac{6}{5}}})

Simplify

lo g_{2} ((4 u v^{3})^{2})

lo g_{e} (\frac{4}{3})

2 lo g_{2} (y - 6) - 4 lo g_{2} (y + 7)

ln (3 ab \cdot 2 c)

\frac{5}{2} (ln (5) - ln (2))

What is 6/5 ln|z-1|-6/5 ln|z+4| ?
The solution to 6/5 ln|z-1|-6/5 ln|z+4| is ln(\sqrt[5]{((z-1)^6)/((z+4)^6)})