6e^3t=9e^2t
This is log work. Not certain what the problem is asking. As written, it is an identity.
6e^3t=9e^2t
e^18t=e^18t
which is hardly an issue.
huh? it's not (e^3t)^6 = (e^2t)^9
6e^3t = 9e^2t
e^t = 9/6
t = log 1.5
To solve the given equation 6e^(3t) = 9e^(2t), we can start by manipulating the equation to isolate the variable 't'. Here's the step-by-step process:
Step 1: Divide both sides of the equation by 9e^(2t) to eliminate the coefficient on the right side:
(6e^(3t))/(9e^(2t)) = 1
Step 2: Simplify by dividing the terms with the same base, e:
(2/3)e^(3t-2t) = 1
Simplifying further, we have:
(2/3)e^t = 1
Step 3: To isolate 't', we need to get rid of the coefficient (2/3). We can do this by multiplying both sides by the reciprocal of (2/3), which is (3/2):
[(2/3)e^t] * (3/2) = 1 * (3/2)
e^t = 3/2
Step 4: Now, to solve for 't', we can take the natural logarithm (ln) of both sides of the equation:
ln(e^t) = ln(3/2)
Step 5: Since the natural logarithm is the inverse function of the exponential function, ln(e^t) cancels out, leaving us with:
t = ln(3/2)
Therefore, the solution to the equation 6e^(3t) = 9e^(2t) is t = ln(3/2).