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

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

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

simplify

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

ln (u^{2} + u^{2} - a^{2}) - ln (a)

Solution steps

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

Apply log rule:

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

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

= ln (u^{2} + u^{2} - a^{2}) - ln (a)

\frac{1}{5} ln (\frac{15}{24})

- \frac{1}{5} lo g_{10} (y + 3) + \frac{1}{5} lo g_{10} (y - 2)

4 lo g_{10} (x - 7) - 5 lo g_{10} (x)

- \frac{1}{3} ln ∣ x + 1 ∣ + \frac{1}{3} ln ∣ x - 2 ∣

lo g_{e} (9) + lo g_{e} (2)

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