What is ln(((x-4)^2)/((x+3)^3)) ?

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

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simplify ln(((x-4)^2)/((x+3)^3))

simplify

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

2 ln (x - 4) - 3 ln (x + 3)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln ((x - 4)^{2}) = 2 ln (x - 4)

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

Apply log rule:

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

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

= 2 ln (x - 4) - 3 ln (x + 3)

0.0259 \cdot ln (\frac{7 \cdot 1 0 ^{15}}{1.5 \cdot 1 0 ^{10}})

ln (20) - ln (2)

lo g_{10} (\frac{1}{e ^{2} e})

5 lo g_{4} (a) - 10 lo g_{4} (b)

\frac{1}{6} lo g_{2} (\frac{1}{6}) + \frac{5}{6} lo g_{2} (\frac{5}{6})

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