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

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

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simplify ln((a+sqrt(a^2+x^2))/x)

simplify

ln (\frac{a + a ^{2} + x ^{2}}{x})

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

Solution steps

ln (\frac{a + a ^{2} + x ^{2}}{x})

Apply log rule:

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

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

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

- ln (3) - ln (x) - ln (5 x)

- lo g_{2} (\frac{1}{10})

\frac{1}{2} ln ∣ 8.7 + 4 ∣ - \frac{1}{2} ln ∣ 8.7 + 6 ∣ + C

\frac{1}{4} \cdot ln (2)

ln (\frac{3}{e})

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