What is simplify-3ln|x+2|-4ln|x+3| ?

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

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simplify-3ln|x+2|-4ln|x+3|

simplify

- 3 ln ∣ x + 2 ∣ - 4 ln ∣ x + 3 ∣

- ln (∣ x + 2 ∣^{3} (x + 3)^{4})

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})

Rewrite

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

- (ln (∣ x + 2 ∣^{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} (ab)

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

= - ln (∣ x + 3 ∣^{4} ∣ x + 2 ∣^{3})

∣ x + 3 ∣^{4} = (x + 3)^{4}

= - ln (∣ x + 2 ∣^{3} (x + 3)^{4})

20 lo g_{42} (2)

(\frac{3}{11}) lo g_{2} (\frac{3}{11}) + (\frac{8}{11}) lo g_{2} (\frac{8}{11})

\frac{1}{1828} ln (\frac{1814}{1828 - 1814})

ln (\frac{87.4}{151.5})

lo g_{8} (3) + 4 lo g_{8} (r)

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