Question

ln(x + 3) − ln(x) = 3. solve analytically??

Answer 1

that was wrong! start with
\[\log(\frac{x+3}{x})=3\] then equivalent exponential form gives
\[\frac{x+3}{x}=10^3\] so
\[\frac{x+3}{x}=1000\]
\[x+3=1000x\] etc

Answer 2

ln [(x + 3)/x] = 3 ===> e^3 = [(x + 3)/x] ===> e^3 (x) =x+3 ==> e^3 (x) -x=3 ==> x(e^3-1)=3 ===> x=3/(e^3-1)

Answer 3

The problem is written as a natural log, so raheen's answer is correct.

Answer 4

ah so it is.

Answer 5

raheen is right

Answer 6

yes raheen is right for sure