What is ln((2x)/(sqrt(x^2-1))) ?

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

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simplify ln((2x)/(sqrt(x^2-1)))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

= 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)

2 ln (5) - 2 ln (2)

\frac{21}{2} + ln (\frac{2}{5})

- lo g_{10} (5.916 \cdot 1 0^{- 5})

ln (- e^{- x} \cdot x^{k})

lo g_{2} (\frac{1}{40})

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