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

The solution to 5ln(2x+2)-4ln(x+1) is ln(32(x+1))

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

simplify

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

ln (32 (x + 1))

Solution steps

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

Apply log rule:

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

5 ln (2 x + 2) = ln ((2 x + 2)^{5})

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

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

Simplify

\frac{( 2 x + 2 ) ^{5}}{( x + 1 ) ^{4}} : 32 (x + 1)

= ln (32 (x + 1))

lo g_{e} (ce)

ln (\frac{1}{x ^{5} y ^{5}})

lo g_{e} (\frac{x + 7}{x + 2})

- lo g_{10} (64 \cdot 1 0^{- 8})

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