How do you solve this equation?
-3e^2t=-480
e^2t = 160
lne^2t = ln(160)
2t = ln(160)
t = ln(160)/2
To solve the equation -3e^(2t) = -480, you need to isolate the variable "t". Here's a step-by-step process to solve this equation:
Step 1: Divide both sides of the equation by -3 to eliminate the coefficient:
(e^(2t)) = -480/-3
(e^(2t)) = 160
Step 2: Take the natural logarithm (ln) of both sides to remove the exponential:
ln(e^(2t)) = ln(160)
2t * ln(e) = ln(160)
Step 3: Simplify the equation:
2t * 1 = ln(160)
2t = ln(160)
Step 4: Finally, divide both sides of the equation by 2 to solve for t:
t = ln(160) / 2
Now, you can use a calculator or software to find the approximate value of t as ln(160) / 2.