Solve the exponential equation. Round the answer to three decimal places if necessary.

Question

e^{x − 5} = 10

Answer 1

Great question, Ben! For this one, we can recall that the natural logarithm (Ln) of a exponential function simply returns the value of the exponent itself. So, you can complete the following steps:

1. Take the natural logarithm of both sides
2. Ln(e^x-5)=Ln(10)
3. The Ln and e cancel each other out, and you have: x-5 = Ln(10)
4. Solve for X
5. X = Ln(10) + 5, or X is approximately 7.303