What is 5ln|x+2|-4ln|x+3| ?

The solution to 5ln|x+2|-4ln|x+3| is ln((|x+2|^5)/((x+3)^4))

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simplify 5ln|x+2|-4ln|x+3|

simplify

5 ln ∣ x + 2 ∣ - 4 ln ∣ x + 3 ∣

ln (\frac{∣ x + 2 ∣ ^{5}}{( x + 3 ) ^{4}})

Solution steps

5 ln ∣ x + 2 ∣ - 4 ln ∣ x + 3 ∣

Apply log rule:

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

5 ln ∣ x + 2 ∣ = ln (∣ x + 2 ∣^{5})

= ln (∣ x + 2 ∣^{5}) - 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 ∣^{5}) - ln (∣ x + 3 ∣^{4})

Apply log rule:

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

ln (∣ x + 2 ∣^{5}) - ln (∣ x + 3 ∣^{4}) = ln (\frac{∣ x + 2 ∣ ^{5}}{∣ x + 3 ∣ ^{4}})

= ln (\frac{∣ x + 2 ∣ ^{5}}{∣ x + 3 ∣ ^{4}})

∣ x + 3 ∣^{4} = (x + 3)^{4}

= ln (\frac{∣ x + 2 ∣ ^{5}}{( x + 3 ) ^{4}})

- lo g_{10} (5.35 \cdot 1 0^{- 4})

7089.884206 \cdot ln (\frac{100 0 ^{2}}{4.5 \cdot 1 0 ^{8}})

ln (\frac{1}{0.5})

2 ln (x) + \frac{1}{2} ln (x^{2} - 4) - 3 ln (\frac{1}{x ^{2} + 2})

ln (7 (n + 1))

What is 5ln|x+2|-4ln|x+3| ?
The solution to 5ln|x+2|-4ln|x+3| is ln((|x+2|^5)/((x+3)^4))