Solve for x. 50e^-0.12x = 10
50e^-0.12x = 10
e^-0.12x = .2
take ln of both sides and use log rules
-.12x ln e = ln .2, remember ln e = 1,
solve for x
To solve for x in the equation 50e^(-0.12x) = 10, you can use logarithms.
Step 1: Divide both sides of the equation by 50 to isolate the exponential term:
e^(-0.12x) = 10/50
e^(-0.12x) = 0.2
Step 2: Take the natural logarithm (ln) of both sides of the equation to remove the exponential term:
ln(e^(-0.12x)) = ln(0.2)
-0.12x = ln(0.2)
Step 3: Divide both sides of the equation by -0.12 to solve for x:
x = ln(0.2) / -0.12
Using a calculator, you can find the decimal value of ln(0.2), which is approximately -1.6094. Then, divide this value by -0.12:
x ≈ -1.6094 / -0.12
x ≈ 13.412
Therefore, the solution is x ≈ 13.412.