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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Combine same powers :

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

ln (\frac{30}{7})

\frac{1}{0.000003} ln (\frac{25 - 15}{75 - 15})

ln ((t^{2} + 1)^{\frac{1}{2}}) + ln (k)

- \frac{1}{9} ln (\frac{100}{5})

ln (\frac{5 + 6}{2 + 3})

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