MHB Solve for x: e^-0.38x=.3 - I Got .4387 - Correct?

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To solve the equation e^(-0.38x) = 0.3, the initial answer of 0.4387 is incorrect. The correct approach involves taking the natural logarithm of both sides, leading to the equation -0.38x = ln(0.3). By rearranging, x can be calculated as ln(0.3) / -0.38, resulting in approximately 3.168. It's recommended to use a scientific calculator or online tools to verify calculations. Understanding how to properly use logarithms is essential for solving exponential equations.
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Solve for x:e^-0.38x=.3
I got .4387 Is that correct
 
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goosey00 said:
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?
 
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=MathJax_Main-Web]−[FONT=MathJax_Main-Web]0.38[FONT=MathJax_Main-Web]∗[FONT=MathJax_Main-Web]0.4387
 
goosey00 said:
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=MathJax_Main-Web]−[FONT=MathJax_Main-Web]0.38[FONT=MathJax_Main-Web]∗[FONT=MathJax_Main-Web]0.4387

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.

$-0.38\ln(x) = ln(0.3)$
 
Hello, goosey00!

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

I got 0.4387 . Is that correct?
Can't you check your answer?
\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
 
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