What is 1/2 ln(x+3)-ln(x) ?

The solution to 1/2 ln(x+3)-ln(x) is ln(((x+3)^{1/2})/x)

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simplify 1/2 ln(x+3)-ln(x)

simplify

\frac{1}{2} ln (x + 3) - ln (x)

ln (\frac{( x + 3 ) ^{\frac{1}{2}}}{x})

Solution steps

\frac{1}{2} ln (x + 3) - ln (x)

Apply log rule:

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

\frac{1}{2} ln (x + 3) = ln ((x + 3)^{\frac{1}{2}})

= ln ((x + 3)^{\frac{1}{2}}) - ln (x)

Apply log rule:

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

ln ((x + 3)^{\frac{1}{2}}) - ln (x) = ln (\frac{( x + 3 ) ^{\frac{1}{2}}}{x})

= ln (\frac{( x + 3 ) ^{\frac{1}{2}}}{x})

ln (9 e^{x})

2 (lo g_{6} (x) + 2 lo g_{6} (y) - 3 lo g_{6} (z))

\frac{1}{3} (3 ln (x + 4) + ln (x) - ln (x^{2} - 5))

2 lo g_{x} (- 3 lo g_{y} (+ 4 lo g_{z} (x)))

lo g_{10} (\frac{y ^{5}}{z ^{2} x ^{3}})

What is 1/2 ln(x+3)-ln(x) ?
The solution to 1/2 ln(x+3)-ln(x) is ln(((x+3)^{1/2})/x)