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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (\frac{20}{40})

ln ∣ x + 2 ∣ + ln ∣ x - 2 ∣

lo g_{9} (\frac{c}{81})

2 ln ∣ x ∣ + 2 ln ∣ x - 3 ∣

3 ln (\frac{x}{y})

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