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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

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Frequently Asked Questions (FAQ)

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