# Math Help - solving for t with natural logs

1. ## solving for t with natural logs

Hello,
I am in differential equations, but it always seems that its my algebra that trips me up. Can anybody tell me how to solve for t in the following expression?:

-8.9 = t - ln(21.34t)

thanks!!
- Jeff

2. Originally Posted by ibanez270dx
Hello,
I am in differential equations, but it always seems that its my algebra that trips me up. Can anybody tell me how to solve for t in the following expression?:

-8.9 = t - ln(21.34t)

thanks!!
- Jeff
This equation doesn't have a real solution:

1. Consider the RHS of the equation as a function in t.

2. This function $f(t)=t-\ln(21.34 \cdot t)$ has an absolute minimum at $M(1, -2.0606)$

3. The graph of f never intersects the graph of y = -8.9

3. thanks! that makes a lot of sense. Now I know that I made an error somewhere along the line. Thanks again!

- Jeff