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

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

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simplify ln(z+sqrt(r^2+z^2))-ln(-z+sqrt(r^2+z^2))

simplify

ln (z + r^{2} + z^{2}) - ln (- z + r^{2} + z^{2})

ln (\frac{( z + r ^{2} + z ^{2} ) ^{2}}{r ^{2}})

Solution steps

ln (z + r^{2} + z^{2}) - ln (- z + r^{2} + z^{2})

Apply log rule:

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

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

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

Simplify

\frac{z + r ^{2} + z ^{2}}{- z + r ^{2} + z ^{2}} : \frac{( z + r ^{2} + z ^{2} ) ^{2}}{r ^{2}}

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

lo g_{a} (\frac{x ^{6}}{y z ^{7}})

lo g_{10} (3 x + 5) - lo g_{10} (x)

2 lo g_{7} (6) + 5 lo g_{7} (d) + 4 lo g_{7} (c)

lo g_{2} (x^{3} y)

7 lo g_{3} (a) + lo g_{3} (b) - 2 lo g_{3} (8 c)

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