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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

3 ln (x + 2) = ln ((x + 2)^{3})

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

Apply log rule:

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

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

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

lo g_{8} ((x y^{2})^{2})

ln (\frac{4000}{500})

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

\frac{6}{5} ln \frac{y}{x} - 1 + ln ∣ x ∣

ln (5 \cdot 1 0^{- 7})

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