I understand the basics, but I can't figure this one out. Any help would be appreciated.

Give the exact answer ( in terms of natural logarithms). Then use a calculator to find an approximat answer.

7.8e^(x/3)ln5 = 14

Thank you for your time.

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- Jan 14th 2008, 01:28 PMTwilightLogarithm help
I understand the basics, but I can't figure this one out. Any help would be appreciated.

Give the exact answer ( in terms of natural logarithms). Then use a calculator to find an approximat answer.

7.8e^(x/3)ln5 = 14

Thank you for your time. - Jan 14th 2008, 02:17 PMtopsquark
- Jan 14th 2008, 02:30 PMTwilight
It is part of the exponent. Sorry that was not clear.

- Jan 14th 2008, 02:54 PMmr fantastic
If the equation is $\displaystyle 7.8 e^{\frac{x \ln 5}{3}} = 14$ then that's one helluva ugly exact answer .......

Picking up from topsquark:

$\displaystyle e^{\frac{x}{3} \ln 5} = \frac{70}{39}$

$\displaystyle \therefore \frac{x}{3} \ln 5 = \ln \frac{70}{39}$

$\displaystyle \therefore x \ln 5 = 3 \ln \frac{70}{39}$

$\displaystyle \therefore x = \frac{3 \ln \frac{70}{39}}{\ln 5}$

$\displaystyle \therefore x = ......$ Only kidding!! log/log CANNOT BE SIMPLIFIED - engrave (*ahem* metaphorically speaking) this fact on your skull.