What is 2ln|x+2|-ln|x+3|+C ?

The solution to 2ln|x+2|-ln|x+3|+C is ln(((x+2)^2)/(|x+3|))+C

Popular >

simplify 2ln|x+2|-ln|x+3|+C

simplify

2 ln ∣ x + 2 ∣ - ln ∣ x + 3 ∣ + C

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

Solution steps

2 ln ∣ x + 2 ∣ - ln ∣ x + 3 ∣ + C

Apply log rule:

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

2 ln ∣ x + 2 ∣ = ln (∣ x + 2 ∣^{2})

= ln (∣ x + 2 ∣^{2}) - ln ∣ x + 3 ∣ + C

Apply log rule:

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

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

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

∣ x + 2 ∣^{2} = (x + 2)^{2}

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

lo g_{5} (y) - 4 lo g_{5} (z)

ln (12.5) + ln (e^{1.6 t})

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

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

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

What is 2ln|x+2|-ln|x+3|+C ?
The solution to 2ln|x+2|-ln|x+3|+C is ln(((x+2)^2)/(|x+3|))+C