# solve for x

#### goosey00

##### Member
Solve for x:e^-0.38x=.3
I got .4387 Is that correct

#### SuperSonic4

##### Well-known member
MHB Math Helper
Solve for x:e^-0.38x=.3
I got .4387 Is that correct
You can check by evaluating $e^{-0.38*0.4387}$
If we use google calculator we end up with 0.8467 (4sf) so 0.4387 is not correct.

What do you know about solving exponential equations and/or the natural logarithm?

#### goosey00

##### Member
I just can't remember how to put it in my calculator again. How did you get the .4387 to times by it-[FONT=MathJax_Math-italic-Web]e[/FONT] [FONT=MathJax_Main-Web]−[/FONT][FONT=MathJax_Main-Web]0.38[/FONT][FONT=MathJax_Main-Web]∗[/FONT][FONT=MathJax_Main-Web]0.4387[/FONT]

#### SuperSonic4

##### Well-known member
MHB Math Helper
I just can't remember how to put it in my calculator again. How did you get the .4387 to times by it-[FONT=MathJax_Math-italic-Web]e[/FONT] [FONT=MathJax_Main-Web]−[/FONT][FONT=MathJax_Main-Web]0.38[/FONT][FONT=MathJax_Main-Web]∗[/FONT][FONT=MathJax_Main-Web]0.4387[/FONT]
Either
Code:
 [2nd] [ln] [(] [-][0.38] [x] [0.4387][)][=]
or
Code:
 [(] [-][0.38] [x] [0.4387][)][2nd] [ln][=]
You can also use an online calculator to check answers - I used google which you can see in the link above and there is also a MHB calculator which works. For your own calculator it may be prudent to find the manual online (search for "Ti30x user manual") so you're not stuck in an exam.

Bear in mind that was just a test to see if your answer was right (it isn't). You need to use the natural logarithm (ln) to find x.

$-0.38\ln(x) = ln(0.3)$

#### soroban

##### Well-known member
Hello, goosey00!

Solve for $$x:\;e^{-0.38x}\:=\:0.3$$

I got 0.4387 . Is that correct?
$$\text{We have: }\:e^{-0.38x} \;=\;0.3$$
$$\text{Take logs: }\:\ln(e^{-0.38x}) \;=\;\ln(0.3) \quad\Rightarrow\quad \text{-}0.38x\underbrace{\ln e}_{\text{This is 1}} \;=\;\ln(0.3)$$
. . . $$\text{-}0.38x \;=\;\ln(0.3) \quad\Rightarrow\quad x \;=\;\frac{\ln(0.3)}{\text{-}0.38}$$
. . . . . $$x \;=\;3.168\,349\,485$$