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Answer :
To solve the equation [tex]\(3 \cdot e^x = 11.76\)[/tex], we'll follow these steps:
1. Isolate the exponential part: Start by dividing both sides of the equation by 3:
[tex]\[
e^x = \frac{11.76}{3}
\][/tex]
This simplifies to:
[tex]\[
e^x = 3.92
\][/tex]
2. Use the natural logarithm to solve for [tex]\(x\)[/tex]: Since the natural logarithm (ln) is the inverse of the exponential function, take the natural logarithm of both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \ln(3.92)
\][/tex]
3. Calculate the natural logarithm: Use a calculator to find the value of [tex]\(\ln(3.92)\)[/tex]. This value is approximately [tex]\(1.3661\)[/tex].
4. Round to two decimal places:
[tex]\[
x \approx 1.37
\][/tex]
Therefore, the solution to the equation [tex]\(3 \cdot e^x = 11.76\)[/tex] is [tex]\(x \approx 1.37\)[/tex].
The correct answer is D. [tex]\(x = 1.37\)[/tex].
1. Isolate the exponential part: Start by dividing both sides of the equation by 3:
[tex]\[
e^x = \frac{11.76}{3}
\][/tex]
This simplifies to:
[tex]\[
e^x = 3.92
\][/tex]
2. Use the natural logarithm to solve for [tex]\(x\)[/tex]: Since the natural logarithm (ln) is the inverse of the exponential function, take the natural logarithm of both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \ln(3.92)
\][/tex]
3. Calculate the natural logarithm: Use a calculator to find the value of [tex]\(\ln(3.92)\)[/tex]. This value is approximately [tex]\(1.3661\)[/tex].
4. Round to two decimal places:
[tex]\[
x \approx 1.37
\][/tex]
Therefore, the solution to the equation [tex]\(3 \cdot e^x = 11.76\)[/tex] is [tex]\(x \approx 1.37\)[/tex].
The correct answer is D. [tex]\(x = 1.37\)[/tex].
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