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Answer :
To solve the equation [tex]\(3 \cdot e^x = 11.76\)[/tex], follow these steps:
1. Isolate the exponential term:
Divide both sides of the equation by 3 to isolate [tex]\(e^x\)[/tex].
[tex]\[
e^x = \frac{11.76}{3}
\][/tex]
2. Calculate the division:
[tex]\[
e^x = 3.92
\][/tex]
3. Solve for [tex]\(x\)[/tex] using natural logarithms:
Take the natural logarithm (ln) of both sides to solve for [tex]\(x\)[/tex].
[tex]\[
x = \ln(3.92)
\][/tex]
4. Calculate the natural logarithm:
Using a calculator or a logarithm table, find [tex]\(\ln(3.92)\)[/tex].
5. Round the result:
The calculated value is approximately [tex]\(1.366\)[/tex]. Rounding this to two decimal places, you get [tex]\(x \approx 1.37\)[/tex].
So, the solution to the equation [tex]\(3 \cdot e^x = 11.76\)[/tex] is [tex]\(x = 1.37\)[/tex].
Therefore, the correct answer is:
D. [tex]\(x=1.37\)[/tex]
1. Isolate the exponential term:
Divide both sides of the equation by 3 to isolate [tex]\(e^x\)[/tex].
[tex]\[
e^x = \frac{11.76}{3}
\][/tex]
2. Calculate the division:
[tex]\[
e^x = 3.92
\][/tex]
3. Solve for [tex]\(x\)[/tex] using natural logarithms:
Take the natural logarithm (ln) of both sides to solve for [tex]\(x\)[/tex].
[tex]\[
x = \ln(3.92)
\][/tex]
4. Calculate the natural logarithm:
Using a calculator or a logarithm table, find [tex]\(\ln(3.92)\)[/tex].
5. Round the result:
The calculated value is approximately [tex]\(1.366\)[/tex]. Rounding this to two decimal places, you get [tex]\(x \approx 1.37\)[/tex].
So, the solution to the equation [tex]\(3 \cdot e^x = 11.76\)[/tex] is [tex]\(x = 1.37\)[/tex].
Therefore, the correct answer is:
D. [tex]\(x=1.37\)[/tex]
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