What is 5ln(x+2)-4ln(x+1) ?

The solution to 5ln(x+2)-4ln(x+1) is ln(((x+2)^5)/((x+1)^4))

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simplify 5ln(x+2)-4ln(x+1)

simplify

5 ln (x + 2) - 4 ln (x + 1)

ln (\frac{( x + 2 ) ^{5}}{( x + 1 ) ^{4}})

Solution steps

5 ln (x + 2) - 4 ln (x + 1)

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 + 1)

Apply log rule:

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

4 ln (x + 1) = ln ((x + 1)^{4})

= ln ((x + 2)^{5}) - ln ((x + 1)^{4})

Apply log rule:

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

ln ((x + 2)^{5}) - ln ((x + 1)^{4}) = ln (\frac{( x + 2 ) ^{5}}{( x + 1 ) ^{4}})

= ln (\frac{( x + 2 ) ^{5}}{( x + 1 ) ^{4}})

ln (\frac{125000000}{599})

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

ln (- 6 e^{x})

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

2 ln (\frac{3}{5})

What is 5ln(x+2)-4ln(x+1) ?
The solution to 5ln(x+2)-4ln(x+1) is ln(((x+2)^5)/((x+1)^4))