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

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

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expand ln(sqrt(((x^2-1))/(x^2+1)))

expand

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

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

Solution steps

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

Rewrite as

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

Apply log rule

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

assuming

x \geq 0

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

cos (x - y) (1 - \frac{d y}{d x})

2 (6 - \frac{4}{3}) π

u (2, 0) v (3, - 4)

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

\frac{s + 2}{( s + 3 ) ( s + 4 )}

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