Solve the exponential equation algebraically: -14 + 3e^x = 11

So I think I move the -14 to the other side, so now I'm left with

3e^x = 25

What do i do next?

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- Oct 12th 2009, 10:48 AMtsmithSolve the exponential equation algebraically?
Solve the exponential equation algebraically: -14 + 3e^x = 11

So I think I move the -14 to the other side, so now I'm left with

3e^x = 25

What do i do next? - Oct 12th 2009, 10:50 AMe^(i*pi)
- Oct 12th 2009, 10:55 AMtsmith
Ok, so

e^x = 25/3

How do I find the natural log of both sides? - Oct 12th 2009, 11:02 AMe^(i*pi)
$\displaystyle ln(x) = log_e(x)$

You don't need to unless you're making a decimal approximation. It is fine to say that $\displaystyle x = ln \left(\frac{25}{3}\right) = 2\ln\left(\frac{5}{3}\right) = 2ln5 - ln3$

Note that I used the laws of logs to simplify. If you're teacher wants you to make a decimal approximation there should be a button marked**ln**on your calculator - Oct 12th 2009, 11:17 AMtsmith
My teacher wants me to round the result to 3 decimal places. What do I type in the calculator?

Thank you for your help, by the way :) - Oct 12th 2009, 11:24 AMe^(i*pi)
$\displaystyle 2*ln(5) - ln(3)$