What is ln((4x)/(2+x^2)) ?

The solution to ln((4x)/(2+x^2)) is 2ln(2)+ln(x)-ln(2+x^2)

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simplify ln((4x)/(2+x^2))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (4 x) = ln (4) + ln (x)

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

ln (4) = 2 ln (2)

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

- lo g_{10} (1.07 \cdot 1 0^{- 6})

- lo g_{10} (1.47 x 1 0^{- 150})

ln (\frac{x}{14})

ln (\frac{5 x - 2 - x sin ( \frac{π x}{2} )}{x ^{2} - 4 x + 6})

ln (x (ln (x))^{x})

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