What is ln(5)+ln(x^2-1)-ln(x-1) ?

The solution to ln(5)+ln(x^2-1)-ln(x-1) is ln(5(x+1))

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simplify ln(5)+ln(x^2-1)-ln(x-1)

simplify

ln (5) + ln (x^{2} - 1) - ln (x - 1)

ln (5 (x + 1))

Solution steps

ln (5) + ln (x^{2} - 1) - ln (x - 1)

Apply log rule:

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

ln (5) + ln (x^{2} - 1) = ln (5 (x^{2} - 1))

= ln (5 (x^{2} - 1)) - ln (x - 1)

Apply log rule:

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

ln (5 (x^{2} - 1)) - ln (x - 1) = ln (\frac{5 ( x ^{2} - 1 )}{x - 1})

= ln (\frac{5 ( x ^{2} - 1 )}{x - 1})

Simplify

\frac{5 ( x ^{2} - 1 )}{x - 1} : 5 (x + 1)

= ln (5 (x + 1))

ln (\frac{y}{c + x})

ln ∣ x ∣ - 2 ln (x + 3)

lo g_{10} (2 5^{\circ}) \cdot 4

3 ln (x) + \frac{1}{3} ln (y)

3 ln (2) - 4 ln (4) - 2 ln (5)

What is ln(5)+ln(x^2-1)-ln(x-1) ?
The solution to ln(5)+ln(x^2-1)-ln(x-1) is ln(5(x+1))