Solve: e^x = 4 sin x

**mathnerd501** · May 5th 2010, 03:21 PM

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.

**surjective** · May 5th 2010, 03:28 PM

Hello,

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

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

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

The x you are searching for is the x-value at the intersection between the graphs of $f$ and $g$ .

**skeeter** · May 5th 2010, 03:53 PM

Originally Posted by mathnerd501

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.

graph $y = e^x - 4\sin{x}$ and calculate the zero(s) in the given interval.

**simplependulum** · May 7th 2010, 05:55 AM

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 $0.5$

Then input

$\ln( 4\sin(Ans) )$ 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 $1.364958434...$

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

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

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