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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Popular Examples

expand log_{4}(((12)/(11^3))^6)expand

lo g_{4} ((\frac{12}{1 1 ^{3}})^{6})

simplify ln(3)-2/3 ln(2)simplify

ln (3) - \frac{2}{3} ln (2)

simplify-0.38*log_{2}(0.38)-0.62log_{2}(0.62)simplify

- 0.38 \cdot lo g_{2} (0.38) - 0.62 lo g_{2} (0.62)

simplify 2*ln(1/(0.8))simplify

2 \cdot ln (\frac{1}{0.8})

simplify log_{e}(1/5)simplify

lo g_{e} (\frac{1}{5})

Frequently Asked Questions (FAQ)

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