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

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

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

simplify

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

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

Solution steps

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

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

ln (e^{i 0}) - ln (3 e^{i 0} + 4)

12 ln (x) - 14 ln (\frac{1}{y}) - 13 ln (x y)

lo g_{c} (m) + lo g_{c} (n)

3 ln (\frac{1}{3})

lo g_{2} (2^{3} 4^{4} 8^{5} l e f t (2^{20})^{22})

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