Answer :

We start with the equation
[tex]$$
1.64\,e^t = 36.9.
$$[/tex]

Step 1. Divide both sides by 1.64

Dividing both sides by 1.64 isolates the exponential term:
[tex]$$
e^t = \frac{36.9}{1.64} = 22.5.
$$[/tex]

Step 2. Take the natural logarithm of both sides

To solve for [tex]$t$[/tex], take the natural logarithm (ln) of both sides:
[tex]$$
\ln(e^t) = \ln(22.5).
$$[/tex]

Using the property that [tex]$\ln(e^t) = t$[/tex], we have:
[tex]$$
t = \ln(22.5).
$$[/tex]

Step 3. Evaluate the natural logarithm

Calculating the natural logarithm gives:
[tex]$$
t \approx 3.1135153092103742.
$$[/tex]

Rounding to four decimal places yields:
[tex]$$
t \approx 3.1135.
$$[/tex]

Thus, the solution to the equation is
[tex]$$
\boxed{3.1135}.
$$[/tex]

Thanks for taking the time to read Solve the equation tex 1 64 e t 36 9 tex tex t square tex Round to four decimal places as needed. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada