Question

solve. provide the exact answer when possible. when not possible round to 4 decimal place.

a) ln(x) +2 = ln(x+3)

(Nina, please be sure to use Ask a New Question instead of piggybacking on another student's post.)

Answer 1

ln(x) +2 = ln(x+3)
replace 2 with ln e^2
ln(x) +ln e^2 = ln(x+3)
ln (xe^2) = ln(x+3)
anti-ln both sides
xe^2 = x+3
xe^2 - x = 3
x(e^2 - 1) = 3
x = 3/(e^2 - 1)

Answer 2

ln x - ln (x+3) = ln [ x/(x+3) ]
so ln [ x/(x+3) ] = -2
remember e^lna = a
so
x/(x+3) = e^-2
now you do it