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

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

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

simplify

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

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

Solution steps

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

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

lo g_{10} (x^{2} y^{4})

lo g_{10} (\frac{a ^{3} b ^{2}}{c ^{4}})

lo g_{\frac{1}{2}} (\frac{3}{4})

4 lo g_{10} (3) + lo g_{10} (2)

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