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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply fractions:

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

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

7 ln (t) - 6 ln (s) + 5 ln (w)

ln (\frac{a}{b ^{3}})

lo g_{10} (\frac{π}{2})

ln (\frac{( w ^{3} )}{z})

ln (2 x) - 2 ln (y) + ln (z)

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