What is simplify-3ln(x+2)+4ln(x+3) ?

The solution to simplify-3ln(x+2)+4ln(x+3) is ln(((x+3)^4)/((x+2)^3))

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simplify-3ln(x+2)+4ln(x+3)

simplify

- 3 ln (x + 2) + 4 ln (x + 3)

ln (\frac{( x + 3 ) ^{4}}{( x + 2 ) ^{3}})

Solution steps

- 3 ln (x + 2) + 4 ln (x + 3)

Apply log rule:

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

3 ln (x + 2) = ln ((x + 2)^{3})

= - ln ((x + 2)^{3}) + 4 ln (x + 3)

Apply log rule:

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

4 ln (x + 3) = ln ((x + 3)^{4})

= - ln ((x + 2)^{3}) + ln ((x + 3)^{4})

Apply log rule:

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

ln ((x + 3)^{4}) - ln ((x + 2)^{3}) = ln (\frac{( x + 3 ) ^{4}}{( x + 2 ) ^{3}})

= ln (\frac{( x + 3 ) ^{4}}{( x + 2 ) ^{3}})

- 4 (ln (4 - v) - ln (4 - u)) + 4 (ln (v) - ln (u))

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

ln (x + 6) - ln (x)

ln (x) - 3 ln (x + 1) - ln (y)

ln (\frac{2 \cdot 1 0 ^{- 6}}{760})

What is simplify-3ln(x+2)+4ln(x+3) ?
The solution to simplify-3ln(x+2)+4ln(x+3) is ln(((x+3)^4)/((x+2)^3))