# Thread: exponential and logarithmic functions

1. ## exponential and logarithmic functions

I am working with this problem:

6 + e^0.5 t = 8

e^0.5 t = 2

0.5 t = ln 2

t = 2 ln 2 I am confused as to how my book got 2 on the right side.

I come up with 1/2. I am wanting to divide each side by 1/2 but the book states to multiply each side by 2. I do not understand.

could someone help please?

thanks!

2. $\displaystyle 6 + e^{\frac{1}{2}t} = 8$

$\displaystyle e^{\frac{1}{2}t} = 2$

NOW, WE TAKE THE NATURAL LOG OF BOTH SIDES AS THE NEXT STEP WILL SHOW:

$\displaystyle \ln({e^{\frac{1}{2}t}}) = \ln{2}$

$\displaystyle \frac{1}{2}t = \ln{2}$

$\displaystyle t = 2\ln{2}$

This is what you should know so you can do these problems:

$\displaystyle e^{\ln{x}} = x$

$\displaystyle \ln{e^x} = x$

So, $\displaystyle e^{\ln{x}} = \ln{e^x} = x$.

Good luck!
-Andy

3. Originally Posted by robasc
I am working with this problem:

...

I am wanting to divide each side by 1/2 but the book states to multiply each side by 2. I do not understand.

could someone help please?

thanks!
Dividing by $\displaystyle \frac12$ is exactly the same as multiplying by 2.

4. so in other words, yo multiply by the reciprocal