What is 4ln|x+5|-ln|x-2|+c ?

The solution to 4ln|x+5|-ln|x-2|+c is ln(((x+5)^4)/(|x-2|))+c

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simplify 4ln|x+5|-ln|x-2|+c

simplify

4 ln ∣ x + 5 ∣ - ln ∣ x - 2 ∣ + c

ln (\frac{( x + 5 ) ^{4}}{∣ x - 2 ∣}) + c

Solution steps

4 ln ∣ x + 5 ∣ - ln ∣ x - 2 ∣ + c

Apply log rule:

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

4 ln ∣ x + 5 ∣ = ln (∣ x + 5 ∣^{4})

= ln (∣ x + 5 ∣^{4}) - ln ∣ x - 2 ∣ + c

Apply log rule:

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

ln (∣ x + 5 ∣^{4}) - ln ∣ x - 2 ∣ = ln (\frac{∣ x + 5 ∣ ^{4}}{∣ x - 2 ∣})

= ln (\frac{∣ x + 5 ∣ ^{4}}{∣ x - 2 ∣}) + c

∣ x + 5 ∣^{4} = (x + 5)^{4}

= ln (\frac{( x + 5 ) ^{4}}{∣ x - 2 ∣}) + c

\frac{ln ( 2 ) 32}{5} - \frac{33}{25}

ln (2.05742) + 0.9 \cdot ln (2.036838)

- lo g_{10} (1.14 \cdot 1 0^{- 6})

- \frac{2 lo g _{10} ( e )}{1 - lo g _{10} ( e )}

ln (x^{2} - 1) - 5 ln (x + 1)

What is 4ln|x+5|-ln|x-2|+c ?
The solution to 4ln|x+5|-ln|x-2|+c is ln(((x+5)^4)/(|x-2|))+c