6e^3t=9e^2t
To solve the equation 6e^3t = 9e^2t, we need to isolate the variable t. Here's how you can do it:
Step 1: Start by dividing both sides of the equation by e^2t. This gives us:
6e^3t / e^2t = 9e^2t / e^2t
Simplifying, we have:
6e^(3t - 2t) = 9
Step 2: Combine the exponents inside the parentheses:
6e^t = 9
Step 3: Divide both sides of the equation by 6:
(6e^t) / 6 = 9 / 6
Simplifying, we get:
e^t = 3/2
Step 4: Take the natural logarithm (ln) of both sides to eliminate the exponential:
ln(e^t) = ln(3/2)
Since ln(e^t) simplifies to t, we have:
t = ln(3/2)
This is the solution to the equation 6e^3t = 9e^2t.