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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], you can follow these steps:
1. Isolate the exponential term:
Start by dividing both sides of the equation by 3 to get the exponential term by itself:
[tex]\[
e^x = \frac{11.76}{3}
\][/tex]
2. Calculate the right-hand side:
Divide 11.76 by 3:
[tex]\[
e^x = 3.92
\][/tex]
3. Use the natural logarithm:
To solve for [tex]\(x\)[/tex], take the natural logarithm (ln) of both sides of the equation. The natural logarithm is the inverse function of the exponential function:
[tex]\[
x = \ln(3.92)
\][/tex]
4. Compute the natural logarithm:
Use a calculator to find the natural logarithm of 3.92, which gives approximately 1.37.
5. Round the result:
Round the solution to two decimal places to match the options provided.
Hence, the solution to the equation [tex]\(3 \cdot e^x = 11.76\)[/tex] is approximately [tex]\(x = 1.37\)[/tex]. Therefore, the correct answer is:
B. [tex]\(x = 1.37\)[/tex]
1. Isolate the exponential term:
Start by dividing both sides of the equation by 3 to get the exponential term by itself:
[tex]\[
e^x = \frac{11.76}{3}
\][/tex]
2. Calculate the right-hand side:
Divide 11.76 by 3:
[tex]\[
e^x = 3.92
\][/tex]
3. Use the natural logarithm:
To solve for [tex]\(x\)[/tex], take the natural logarithm (ln) of both sides of the equation. The natural logarithm is the inverse function of the exponential function:
[tex]\[
x = \ln(3.92)
\][/tex]
4. Compute the natural logarithm:
Use a calculator to find the natural logarithm of 3.92, which gives approximately 1.37.
5. Round the result:
Round the solution to two decimal places to match the options provided.
Hence, the solution to the equation [tex]\(3 \cdot e^x = 11.76\)[/tex] is approximately [tex]\(x = 1.37\)[/tex]. Therefore, the correct answer is:
B. [tex]\(x = 1.37\)[/tex]
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