1. stuck on Logarithmic equation

Im stuck on this one. I can't figure out the next step. if I devide through by x it gets confusing. could someone show a next step.

thanks.

$\displaystyle \ln \left( x+2 \right) =1+\ln \left( x \right)$

i get to here...

$\displaystyle {\frac {x+2}{x}}={{\rm e}}$

this is the solution in the book.

$\displaystyle x={\frac {2}{\rm e-1}}$

2. Originally Posted by skoker
Im stuck on this one. I can't figure out the next step. if I devide through by x it gets confusing. could someone show a next step.

thanks.

$\displaystyle \ln \left( x+2 \right) =1+\ln \left( x \right)$

i get to here...

$\displaystyle {\frac {x+2}{x}}={{\rm e}}$

this is the solution in the book.

$\displaystyle x={\frac {2}{\rm e-1}}$
Dear skoker,

Subject x in your equation. For that first you need to multiply both sides by x.

3. ok i think i got it. i have to factor out x.

$\displaystyle x+2={{\rm e}}x$

$\displaystyle 2=x \left \left( e-1 \right)$

$\displaystyle x={\frac {2}{\rm e-1}}$

thanks.

4. An alternative:

$\displaystyle \displaystyle \frac{x + 2}{x} = e$

$\displaystyle \displaystyle 1 + \frac{2}{x} = e$

$\displaystyle \displaystyle \frac{2}{x} = e-1$

$\displaystyle \displaystyle \frac{x}{2} = \frac{1}{e-1}$

$\displaystyle \displaystyle x = \frac{2}{e-1}$.

5. ah. thats good you posted that. I was trying to figure a way to do it without multiplying through with x. I did not think of flipping both sides like that. interesting.