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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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Frequently Asked Questions (FAQ)

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