# Thread: Solve the exponential equation algebraically?

1. ## Solve 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?

2. Originally Posted by tsmith
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?
1. Divide both sides by 3
2. Take the natural log of both sides. Do not use a decimal approximation

3. Ok, so
e^x = 25/3
How do I find the natural log of both sides?

4. Originally Posted by tsmith
Ok, so
e^x = 25/3
How do I find the natural log of both sides?
$\displaystyle ln(x) = log_e(x)$

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

5. 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

6. $\displaystyle 2*ln(5) - ln(3)$