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

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

Popular >

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

simplify

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

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

Solution steps

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

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

Apply log rule:

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

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

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

Simplify

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

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

3 lo g_{10} (m) + 2 lo g_{10} (n)

ln (2) - ln (- 1)

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

ln (\frac{2}{12})

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

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