# Logarithm help

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• January 14th 2008, 01:28 PM
Twilight
Logarithm 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.
• January 14th 2008, 02:17 PM
topsquark
Quote:

Originally Posted by Twilight
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.

If you want an exact answer then turn the decimal into a fraction first:
$7.8 = \frac{78}{10} = \frac{39}{5}$

My question, though, is whether the "ln(5)" is part of the exponent, or multiplying the e^(x/3)?

-Dan
• January 14th 2008, 02:30 PM
Twilight
It is part of the exponent. Sorry that was not clear.
• January 14th 2008, 02:54 PM
mr fantastic
Quote:

Originally Posted by Twilight
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.

If the equation is $7.8 e^{\frac{x \ln 5}{3}} = 14$ then that's one helluva ugly exact answer .......

Picking up from topsquark:

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

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

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

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

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