What is ln(x)-1/2 ln(x^2+9) ?

The solution to ln(x)-1/2 ln(x^2+9) is ln((xsqrt(x^2+9))/(x^2+9))

Popular >

simplify ln(x)-1/2 ln(x^2+9)

simplify

ln (x) - \frac{1}{2} ln (x^{2} + 9)

ln (\frac{x x ^{2} + 9}{x ^{2} + 9})

Solution steps

ln (x) - \frac{1}{2} ln (x^{2} + 9)

Apply log rule:

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

\frac{1}{2} ln (x^{2} + 9) = ln ((x^{2} + 9)^{\frac{1}{2}})

= ln (x) - ln ((x^{2} + 9)^{\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} + 9)^{\frac{1}{2}}) = ln (\frac{x}{( x ^{2} + 9 ) ^{\frac{1}{2}}})

= ln (\frac{x}{( x ^{2} + 9 ) ^{\frac{1}{2}}})

Simplify

\frac{x}{( x ^{2} + 9 ) ^{\frac{1}{2}}} : \frac{x x ^{2} + 9}{x ^{2} + 9}

= ln (\frac{x x ^{2} + 9}{x ^{2} + 9})

4 ln (x) - ln (1 + x) + ln (1 - x)

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

ln (\frac{100 + 1.84}{1.84})

\frac{3}{2} (ln (11) - ln (3))

- lo g_{10} (6.21 \cdot 1 0^{- 5})

What is ln(x)-1/2 ln(x^2+9) ?
The solution to ln(x)-1/2 ln(x^2+9) is ln((xsqrt(x^2+9))/(x^2+9))