What is ln(sqrt((a^2-z^2)/(a^2+z^2))) ?

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

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simplify ln(sqrt((a^2-z^2)/(a^2+z^2)))

simplify

ln (\frac{a ^{2} - z ^{2}}{a ^{2} + z ^{2}})

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

Solution steps

ln (\frac{a ^{2} - z ^{2}}{a ^{2} + z ^{2}})

Rewrite as

= ln ((\frac{a ^{2} - z ^{2}}{a ^{2} + z ^{2}})^{\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{- z ^{2} + a ^{2}}{z ^{2} + a ^{2}})

x \to 5 lim (\frac{x - 5}{x - 5})

\int \frac{1}{4 x ^{2} - 4 x + 5} d x

\frac{d y}{d x} tan (y) = \frac{1}{x}

x \to 1 lim (18 x^{100} - 5)

\int_{1}^{3} (3 x^{2} + 4) d x

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