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}})

∣ x + 3 ∣^{4} = (x + 3)^{4}

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

20 lo g_{10} (4 π) - 20 lo g_{10} (300000)

- ln ∣ x + 2 ∣ + 2 ln ∣ x - 3 ∣ + C

1 \cdot lo g_{10} (0.65) + (1 - 1) \cdot lo g_{10} (1 - 0.65)

ln (x) + ln (y) + 2 ln (12 - x - y)

ln (\frac{x}{( x + 1 )})

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))