1. ## 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

2. 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

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

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

-Dan

3. It is part of the exponent. Sorry that was not clear.

4. 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

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.