What is 4ln(x-4)+5ln(x-5)+c ?

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

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simplify 4ln(x-4)+5ln(x-5)+c

simplify

4 ln (x - 4) + 5 ln (x - 5) + c

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

Solution steps

4 ln (x - 4) + 5 ln (x - 5) + c

Apply log rule:

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

4 ln (x - 4) = ln ((x - 4)^{4})

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

Apply log rule:

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

5 ln (x - 5) = ln ((x - 5)^{5})

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

ln (\frac{x ^{3} y ^{2}}{z ^{5}})

- ln (\frac{2.8}{5}) \cdot 52.41

ln (- \frac{5}{4} e^{4 x})

3 (ln (3 e))^{2} + 2 ln (3 e)

- lo g_{10} (1.5 \cdot 1 0^{- 9})

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