Solve the equation, e^x=4sinx ; x is greater than 0, less than 2pi.

how do i figure this out, and i have my ti-83 with me.

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- May 5th 2010, 03:21 PMmathnerd501Solve: e^x = 4 sin x
Solve the equation, e^x=4sinx ; x is greater than 0, less than 2pi.

how do i figure this out, and i have my ti-83 with me. - May 5th 2010, 03:28 PMsurjectiveequation
Hello,

If you use your TI-83, you could simply punch in the function:

$\displaystyle f(x)=e^{x}$

$\displaystyle g(x)=4\sin(x)$

The x you are searching for is the x-value at the intersection between the graphs of $\displaystyle f$ and $\displaystyle g$. - May 5th 2010, 03:53 PMskeeter
- May 7th 2010, 05:55 AMsimplependulum
Can you input 'Ans' in your calculator (portable)? That means it can memorize the value obtained before and use the value in other calculation.

Set it to be about $\displaystyle 0.5 $

Then input

$\displaystyle \ln( 4\sin(Ans) ) $ and press ' Enter' followed by ' Enter' ,' Enter',' Enter',' Enter',.... until no observable change on the screen , then the value displayed on it is the solution . It is $\displaystyle 1.364958434...$

The key to find out the solution is to put one of the variable $\displaystyle x $ as the subject . Here we can put $\displaystyle x = \ln(4\sin(x))$ or $\displaystyle x = \sin^{-1}(\frac{e^x}{4})$

I also obtain the other solution , $\displaystyle 0.370558096...$