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Answer :
Sure, let's solve the equation step-by-step:
We start with the equation:
[tex]\[ 3 \cdot e^x = 11.76 \][/tex]
1. Isolate [tex]\( e^x \)[/tex]:
[tex]\[ e^x = \frac{11.76}{3} \][/tex]
[tex]\[ e^x = 3.92 \][/tex]
2. Take the natural logarithm (ln) of both sides to solve for [tex]\( x \)[/tex]:
[tex]\[ \ln(e^x) = \ln(3.92) \][/tex]
[tex]\[ x = \ln(3.92) \][/tex]
3. Calculate [tex]\( \ln(3.92) \)[/tex]:
This is a calculation that you would typically use a calculator for. The natural logarithm of 3.92 is approximately 1.367.
4. Round to two decimal places:
[tex]\[ x \approx 1.37 \][/tex]
So, the solution to the equation [tex]\( 3 \cdot e^x = 11.76 \)[/tex], rounded to two decimal places, is:
[tex]\[ x = 1.37 \][/tex]
Therefore, the correct option is:
[tex]\[ \boxed{x = 1.37} \][/tex]
Option D is the correct answer.
We start with the equation:
[tex]\[ 3 \cdot e^x = 11.76 \][/tex]
1. Isolate [tex]\( e^x \)[/tex]:
[tex]\[ e^x = \frac{11.76}{3} \][/tex]
[tex]\[ e^x = 3.92 \][/tex]
2. Take the natural logarithm (ln) of both sides to solve for [tex]\( x \)[/tex]:
[tex]\[ \ln(e^x) = \ln(3.92) \][/tex]
[tex]\[ x = \ln(3.92) \][/tex]
3. Calculate [tex]\( \ln(3.92) \)[/tex]:
This is a calculation that you would typically use a calculator for. The natural logarithm of 3.92 is approximately 1.367.
4. Round to two decimal places:
[tex]\[ x \approx 1.37 \][/tex]
So, the solution to the equation [tex]\( 3 \cdot e^x = 11.76 \)[/tex], rounded to two decimal places, is:
[tex]\[ x = 1.37 \][/tex]
Therefore, the correct option is:
[tex]\[ \boxed{x = 1.37} \][/tex]
Option D is the correct answer.
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