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.