What is simplify-ln|x-2|+4ln|x+5|+C ?

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

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

simplify

- ln ∣ x - 2 ∣ + 4 ln ∣ x + 5 ∣ + C

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

Solution steps

- ln ∣ x - 2 ∣ + 4 ln ∣ x + 5 ∣ + C

Apply log rule:

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

4 ln ∣ x + 5 ∣ = ln (∣ x + 5 ∣^{4})

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

ln (\frac{4}{x})

8 lo g_{10} (c) + 8 lo g_{10} (a) - 4 lo g_{10} (b)

ln (cos (x)) - ln (cos (y))

3 lo g_{5} (u) + 4 lo g_{5} (v)

ln (\frac{0.0521}{0.101})

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