how do i solve for t:
-.50=1-e^-(t/125)^5
i got this far:
ln(.5)=5ln(-t/125)
t=?
5 e^-(t/5^2) = 1.5
e^-(t/125) = .3
e^(t/125) = 1/.3 = 3.3333
t/125 = ln 3.3333
t = 150.5
To solve for t in the equation -.50 = 1 - e^-(t/125)^5, you have made some progress by taking the natural logarithm of both sides. However, there seems to be a slight mistake in your work. Let's go through the solution step-by-step.
Starting with the original equation:
-.50 = 1 - e^-(t/125)^5
First, subtract 1 from both sides:
-1.50 = -e^-(t/125)^5
Next, multiply both sides by -1 to make the equation positive:
1.50 = e^-(t/125)^5
Now, take the natural logarithm (ln) of both sides:
ln(1.50) = ln[e^-(t/125)^5]
Here, you need to remember the logarithmic property that ln(e^x) = x. Applying this property, the equation becomes:
ln(1.50) = -(t/125)^5
Finally, to solve for t, raise both sides as a power of 1/5:
[(ln(1.50)]^(1/5) = -t/125
To isolate t, multiply both sides by -125:
t = -125 * [(ln(1.50)]^(1/5)
So, the solution for t is t = -125 * [(ln(1.50)]^(1/5).
Remember to use a calculator to compute the value of ln(1.50) and evaluate the expression [(ln(1.50)]^(1/5) to get the numerical solution for t.