# Thread: Exponentiating both sides of an equation.

1. ## Exponentiating both sides of an equation.

$\displaystyle ln(y+1)+ln(y-1)=2x+ln(x)$

So if both sides are exponentiated with base e then the resulting left side of the equation comes out to by my solutions manual:

$\displaystyle (y+1)*(y-1)$

I am wondering by what arithmetic or property that the "+" on the left hand side of the equation turned into a "*" or a multiplication.

The whole equation turns out to be:

$\displaystyle (y+1)*(y-1)=e^(^2^x^)*x$

Thanks for any responses...

2. ## Re: Exponentiating both sides of an equation.

Hey sepoto.

Basically the reason why has to do with the properties of exponentials where e^(a+b) = e^a * e^b. This is where the multiplication property comes in.

3. ## Re: Exponentiating both sides of an equation.

I probably haven't understood your question but it gave me a chance to practice LaTeX anyway.
Maybe it will help

\displaystyle \begin{align*} \text {RHS}&=e^{2x+lnx}\\&=e^{2x}\times e^{lnx}\\&=e^{2x} \times x\\&=xe^{2x}\end{align*}