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Popular >

simplify 2ln(x-1)+3ln(x+1)

Solution

simplify

2 ln (x - 1) + 3 ln (x + 1)

Solution

ln ((x - 1)^{2} (x + 1)^{3})

Solution steps

2 ln (x - 1) + 3 ln (x + 1)

Apply log rule:

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

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

= ln ((x - 1)^{2}) + 3 ln (x + 1)

Apply log rule:

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

3 ln (x + 1) = ln ((x + 1)^{3})

= ln ((x - 1)^{2}) + ln ((x + 1)^{3})

Apply log rule:

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

ln ((x - 1)^{2}) + ln ((x + 1)^{3}) = ln ((x + 1)^{3} (x - 1)^{2})

= ln ((x - 1)^{2} (x + 1)^{3})

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Frequently Asked Questions (FAQ)

What is 2ln(x-1)+3ln(x+1) ?
The solution to 2ln(x-1)+3ln(x+1) is ln((x-1)^2(x+1)^3)