What is ln(((x-2)^5)/((x+1)^3)) ?

The solution to ln(((x-2)^5)/((x+1)^3)) is 5ln(x-2)-3ln(x+1)

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simplify ln(((x-2)^5)/((x+1)^3))

simplify

ln (\frac{( x - 2 ) ^{5}}{( x + 1 ) ^{3}})

5 ln (x - 2) - 3 ln (x + 1)

Solution steps

ln (\frac{( x - 2 ) ^{5}}{( x + 1 ) ^{3}})

Apply log rule:

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

ln (\frac{( x - 2 ) ^{5}}{( x + 1 ) ^{3}}) = ln ((x - 2)^{5}) - ln ((x + 1)^{3})

= ln ((x - 2)^{5}) - ln ((x + 1)^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 5 ln (x - 2) - ln ((x + 1)^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x + 1)^{3}) = 3 ln (x + 1)

= 5 ln (x - 2) - 3 ln (x + 1)

4 lo g_{10} (x) - \frac{1}{3} (x^{2} + 1) + 2 lo g_{10} (x - 1)

6 ln (\frac{5}{2}) - \frac{9}{5}

lo g_{9} (\frac{1}{6})

ln (\frac{821.85}{1643}) \cdot 8

ln (\frac{11}{9})

What is ln(((x-2)^5)/((x+1)^3)) ?
The solution to ln(((x-2)^5)/((x+1)^3)) is 5ln(x-2)-3ln(x+1)