Solve for x correct to four decimal places: e^(5x) = 7.8

Bear with me, ya'll. Just trying to study for a cumulative final in which I don't remember anything. :-)

Question

Solve for x correct to four decimal places:  e^(5x) = 7.8 

Bear with me, ya'll. Just trying to study for a cumulative final in which I don't remember anything. :-)

sunnnystrong · Answer

$$e^{5x}=7.8$$
Okay: to solve for x --> we need to take the natural log of both sides.
(inverse function of exponent)
Natural log is best choice because base e.
$$ln e^{5x}=ln 7.8$$
$$5x=ln( 7.8)$$

Solve for x --->

x=?

stephanieelizzz · Answer

.4108? :)

sunnnystrong · Answer

@stephanieelizzz yep!
:D

stephanieelizzz · Answer

I realize this is a simpler one of these problems, but for example if there was a number before e, would it affect the way the bases cancel each other? @sunnnystrong

sunnnystrong · Answer

Hmm... yes. 
Basic Facts:
$$\ln(e)=1$$

Lets say that number was 2 and not e -->

$$2^{5x}=7.8$$
Take the natural log -->
$$5x*\ln(2)=\ln(7.8)$$

Than solve for x.

stephanieelizzz · Answer

Got it! Thank you :)