Solving for x in an exponential

[meorozco]

Homework Statement

My problem is: e^-(xt) <= y, where t = 10 and y = 10^-6

So: e^-(x10) <= 10^-6

I have to find a value x that would make the probabilty less than or equal to 10^-6.

Homework Equations

The Attempt at a Solution

I am not sure but my attempt in finding x is:

x*10 =ln(10^-6)
x=ln(10^-6) / 10

I am not so sure that is right. I'm having somewhat of difficulty treating the e in the problem. Any help is greatly appreciated. Thanks

 

[danago]

Thats right in taking natural logs of both sides to start with, but you seem to have missed a negative sign in your first step.

 

[meorozco]

Ok, so I would get ln(-x*10) <= ln 10^-6
x = ln(10^-6) / -10)
If I do that I calculate x to be 13.8. Does this seem right?
Put x= 13.8 back into the original equation. Does it satisfy the equation?

 

[hotvette]

In problems like this, you can always confirm your answer by going back to the original equation. Since you've found x and you know t, just calculate e^-xt and see if it gives the answer you want.
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