Homework Help: E^-x, solve for x

1. Dec 3, 2011

ZedCar

1. The problem statement, all variables and given/known data
Solve for x

0.5y = e^-x

3. The attempt at a solution

I believe the answer is x = ln(2/y)

Would anyone be able to explain the intermediate steps please?

If I was trying it I would have got -ln0.5y = x

2. Dec 3, 2011

Curious3141

Your answer is right, and you can easily rearrange it to ln (2/y).

What is the relationship between -ln (a) and ln (a)?

3. Dec 3, 2011

cbetanco

If you take the log of either side you get

$ln(y/2)=-x$ or rearranging terms and using $ln(a/b)=ln(a)-ln(b)$ gives $x=-ln(y/2)=-(ln(y)-ln(2))=ln(2/y)$

4. Dec 3, 2011

Mentallic

Or more simply,

$$a\cdot \ln(b)=\ln(b^a)$$

so

$$-\ln(y)=\ln(y^{-1})=\ln(1/y)$$

5. Dec 3, 2011

ZedCar

Thanks very much guys!

6. Dec 3, 2011

Staff: Mentor

Or, -ln(y) = 0 - ln(y) = ln(1) - ln(y) = ln(1/y).

Here, I'm using the property that ln(a/b) = ln(a) - ln(b) (in reverse).