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Popular >

simplify ln((e^{4x})/(x^2+1))

Solution

simplify

ln (\frac{e ^{4 x}}{x ^{2} + 1})

Solution

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

Solution steps

ln (\frac{e ^{4 x}}{x ^{2} + 1})

Apply log rule:

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

ln (\frac{e ^{4 x}}{x ^{2} + 1}) = ln (e^{4 x}) - ln (x^{2} + 1)

= ln (e^{4 x}) - ln (x^{2} + 1)

Apply log rule:

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

ln (e^{4 x}) = 4 x ln (e)

= 4 x ln (e) - ln (x^{2} + 1)

4 x ln (e) = 4 x

= 4 x - ln (x^{2} + 1)

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Frequently Asked Questions (FAQ)

What is ln((e^{4x})/(x^2+1)) ?
The solution to ln((e^{4x})/(x^2+1)) is 4x-ln(x^2+1)