Solve 40e^(0.6x) - 3=237
40e^(0.6x) - 3=237
40e^(.6x) = 240
e^.6x = 6
ln both sides
ln e^.6x = ln 6
.6x ln e = ln 6
.6x = ln 6 , remember ln e = 1
x = ln 6/.6
= appr 2.986
To solve the equation 40e^(0.6x) - 3 = 237, we can follow the steps below:
Step 1: Start by isolating the exponential term.
Add 3 to both sides of the equation:
40e^(0.6x) = 240
Step 2: Divide both sides of the equation by 40 to isolate the exponential term further:
e^(0.6x) = 6
Step 3: Take the natural logarithm (ln) of both sides of the equation. This will help us get rid of the exponential term:
ln(e^(0.6x)) = ln(6)
Step 4: Apply the logarithm property, which states that ln(e^a) is equal to a:
0.6x = ln(6)
Step 5: Finally, divide both sides by 0.6 to solve for x:
x = ln(6) / 0.6
Using a calculator, we can compute the value of x:
x ≈ 2.872
So, the solution to the equation "40e^(0.6x) - 3 = 237" is x ≈ 2.872.