What is 1/2 ln(1+x^2)-ln(x) ?

The solution to 1/2 ln(1+x^2)-ln(x) is ln(((1+x^2)^{1/2})/x)

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simplify 1/2 ln(1+x^2)-ln(x)

simplify

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

ln \frac{( 1 + x ^{2} ) ^{\frac{1}{2}}}{x}

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} ln (x^{2} + 1) = ln ((x^{2} + 1)^{\frac{1}{2}})

= ln ((x^{2} + 1)^{\frac{1}{2}}) - ln (x)

Apply log rule:

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

ln ((1 + x^{2})^{\frac{1}{2}}) - ln (x) = ln \frac{( x ^{2} + 1 ) ^{\frac{1}{2}}}{x}

= ln \frac{( 1 + x ^{2} ) ^{\frac{1}{2}}}{x}

lo g_{e} (x sin (x))

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ln ((y + 10)^{2} y - 5)

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

ln (x + 6) - ln (x - 4)

What is 1/2 ln(1+x^2)-ln(x) ?
The solution to 1/2 ln(1+x^2)-ln(x) is ln(((1+x^2)^{1/2})/x)