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Answer :
To solve the equation [tex]\(3 \cdot e^x = 11.76\)[/tex] and find the value of [tex]\(x\)[/tex], follow these steps:
1. Divide both sides by 3:
[tex]\[
e^x = \frac{11.76}{3}
\][/tex]
Simplifying the right side gives:
[tex]\[
e^x = 3.92
\][/tex]
2. Take the natural logarithm (ln) of both sides to solve for [tex]\(x\)[/tex]. The property you'll use here is that if [tex]\(e^x = a\)[/tex], then [tex]\(x = \ln(a)\)[/tex]. So, apply this property:
[tex]\[
x = \ln(3.92)
\][/tex]
3. Calculate the natural logarithm:
[tex]\[
x \approx 1.366091653802371
\][/tex]
4. Round the result to two decimal places:
[tex]\[
x \approx 1.37
\][/tex]
Thus, the solution to the equation [tex]\(3 \cdot e^x = 11.76\)[/tex], rounded to two decimal places, is [tex]\(x = 1.37\)[/tex].
Hence, the correct answer is:
C. [tex]\(x = 1.37\)[/tex]
1. Divide both sides by 3:
[tex]\[
e^x = \frac{11.76}{3}
\][/tex]
Simplifying the right side gives:
[tex]\[
e^x = 3.92
\][/tex]
2. Take the natural logarithm (ln) of both sides to solve for [tex]\(x\)[/tex]. The property you'll use here is that if [tex]\(e^x = a\)[/tex], then [tex]\(x = \ln(a)\)[/tex]. So, apply this property:
[tex]\[
x = \ln(3.92)
\][/tex]
3. Calculate the natural logarithm:
[tex]\[
x \approx 1.366091653802371
\][/tex]
4. Round the result to two decimal places:
[tex]\[
x \approx 1.37
\][/tex]
Thus, the solution to the equation [tex]\(3 \cdot e^x = 11.76\)[/tex], rounded to two decimal places, is [tex]\(x = 1.37\)[/tex].
Hence, the correct answer is:
C. [tex]\(x = 1.37\)[/tex]
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