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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln ((x - 2)^{3}) = 3 ln (x - 2)

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

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

Apply log rule:

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

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

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

ln (\frac{373}{298})

ln (\frac{1}{48})

lo g_{10} (\frac{x}{10 x ^{2}})

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

lo g_{8} (\frac{1}{6})

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