Answer :

We start with the equation
[tex]$$
2.39 e^t = 36.3.
$$[/tex]

Step 1. Divide both sides of the equation by [tex]$2.39$[/tex] to isolate [tex]$e^t$[/tex]:
[tex]$$
e^t = \frac{36.3}{2.39}.
$$[/tex]

Step 2. Calculate the division:
[tex]$$
e^t \approx 15.1883.
$$[/tex]

Step 3. To solve for [tex]$t$[/tex], take the natural logarithm of both sides. Recall that [tex]$\ln(e^t) = t$[/tex], so:
[tex]$$
t = \ln\left(\frac{36.3}{2.39}\right) \approx \ln(15.1883).
$$[/tex]

Step 4. Evaluating the logarithm gives:
[tex]$$
t \approx 2.720524375327386.
$$[/tex]

Step 5. Finally, rounding [tex]$t$[/tex] to four decimal places, we have:
[tex]$$
t \approx 2.7205.
$$[/tex]

Thus, the solution to the equation is
[tex]$$
\boxed{2.7205}.
$$[/tex]

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Rewritten by : Barada