Finding X in the Exponent

**OnMyWayToBeAMathProffesor** · November 27th 2007, 04:51 PM

I am stuck on these three problems. I have to find out what x is. Any help would be greatly appreciated.

$1.06^x=4.1$

$50e^{.035x}=200$

$3+2e^{-x}=6$

Thank you!

**FalconPUNCH!** · November 27th 2007, 04:52 PM

Hmm...I'm not sure if this is right but I'd probably take the natural log of both sides.

**OnMyWayToBeAMathProffesor** · November 27th 2007, 05:00 PM

so i should divide $\frac{ln{4.1}}{ln{1.06^x}}$ but that gives me 24.21609205, which could not be X. or did i do this wrong? same thing for the other problems?

**FalconPUNCH!** · November 27th 2007, 05:05 PM

Originally Posted by OnMyWayToBeAMathProffesor

so i should divide $\frac{ln{4.1}}{ln{1.06^x}}$ but that gives me 24.21609205, which could not be X. or did i do this wrong? same thing for the other problems?

No it should turn out to be

$ln1.06^x = ln4.1$

$(x)ln1.06 = ln4.1$ because of the power rule

$x = \frac {ln4.1}{ln1.06}$

and just use a calculator to solve that. Well it did come out to be the same answer. Idk because I'm not a helper, so you should ask someone else.

**OnMyWayToBeAMathProffesor** · November 27th 2007, 05:09 PM

i am sorry, i did not mean to type the X in the ln equation. i did $\frac{ln{4.1}}{ln{1.06}}$ and got 24.21509205. Thanks for your help anyway.

Anybody else know?

**FalconPUNCH!** · November 27th 2007, 05:09 PM

Originally Posted by OnMyWayToBeAMathProffesor

i am sorry, i did not mean to type the X in the ln equation. i did $\frac{ln{4.1}}{ln{1.06}}$ and got 24.21509205. Thanks for your help anyway.

Anybody else know?

I checked and it seems to be the correct answer.

**OnMyWayToBeAMathProffesor** · November 27th 2007, 05:15 PM

so if X=24.21609205 than $1.06^{24.21609205}$ should equal 4.1 but actually equals 1.079758817.

any ideas?

**FalconPUNCH!** · November 27th 2007, 05:16 PM

Originally Posted by OnMyWayToBeAMathProffesor

so if X=24.21609205 than $1.06^{24.21609205}$ should equal 4.1 but actually equals 1.079758817.

any ideas?

Really? I get approximately 4.1

**OnMyWayToBeAMathProffesor** · November 27th 2007, 05:20 PM

o, i forgot to add the parenthesis. Thank you very much for all of your gracious help. Would i employ the same technique to find out the other 2,

$50e^{.035x}=200$

$3+2e^{-x}=6$

Once again, many thanks.

**FalconPUNCH!** · November 27th 2007, 05:31 PM

Originally Posted by OnMyWayToBeAMathProffesor

o, i forgot to add the parenthesis. Thank you very much for all of your gracious help. Would i employ the same technique to find out the other 2,

$50e^{.035x}=200$

$3+2e^{-x}=6$

Once again, many thanks.

Yes it should work too. Just remember that $ln(e) = 1$

**OnMyWayToBeAMathProffesor** · November 27th 2007, 05:37 PM

thank you.

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