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

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

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simplify ln(x^2-1)-2ln(x+1)+ln(x^2+x)

simplify

ln (x^{2} - 1) - 2 ln (x + 1) + ln (x^{2} + x)

ln (x (x - 1))

Solution steps

ln (x^{2} - 1) - 2 ln (x + 1) + ln (x^{2} + x)

Apply log rule:

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

2 ln (x + 1) = ln ((x + 1)^{2})

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{2} - 1}{( x + 1 ) ^{2}} : \frac{x - 1}{x + 1}

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

Apply log rule:

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

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

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

Simplify

\frac{x - 1}{x + 1} (x^{2} + x) : x (x - 1)

= ln (x (x - 1))

lo g_{10} (x^{3} z)

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

\frac{9 ln ( 5 )}{2 ln ( 3 ) - ln ( 5 )}

lo g_{10} (3 x + 10) - lo g_{10} (x)

lo g_{10} (a) + 4 lo g_{10} (b)

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