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Answer :
We start with the equation
[tex]$$3 \cdot e^x = 11.76.$$[/tex]
Step 1. Isolate [tex]\( e^x \)[/tex]:
Divide both sides of the equation by 3:
[tex]$$e^x = \frac{11.76}{3} = 3.92.$$[/tex]
Step 2. Solve for [tex]\( x \)[/tex]:
Take the natural logarithm on both sides to solve for [tex]\( x \)[/tex]:
[tex]$$\ln(e^x) = \ln(3.92).$$[/tex]
Since [tex]\( \ln(e^x) = x \)[/tex], we get
[tex]$$x = \ln(3.92).$$[/tex]
Step 3. Round the result:
Evaluating [tex]\( \ln(3.92) \)[/tex] gives approximately [tex]\( 1.366091653802371 \)[/tex]. Rounding to two decimal places, we have
[tex]$$x \approx 1.37.$$[/tex]
Thus, the solution to the equation rounded to two decimal places is [tex]\( \boxed{1.37} \)[/tex], which corresponds to answer choice D.
[tex]$$3 \cdot e^x = 11.76.$$[/tex]
Step 1. Isolate [tex]\( e^x \)[/tex]:
Divide both sides of the equation by 3:
[tex]$$e^x = \frac{11.76}{3} = 3.92.$$[/tex]
Step 2. Solve for [tex]\( x \)[/tex]:
Take the natural logarithm on both sides to solve for [tex]\( x \)[/tex]:
[tex]$$\ln(e^x) = \ln(3.92).$$[/tex]
Since [tex]\( \ln(e^x) = x \)[/tex], we get
[tex]$$x = \ln(3.92).$$[/tex]
Step 3. Round the result:
Evaluating [tex]\( \ln(3.92) \)[/tex] gives approximately [tex]\( 1.366091653802371 \)[/tex]. Rounding to two decimal places, we have
[tex]$$x \approx 1.37.$$[/tex]
Thus, the solution to the equation rounded to two decimal places is [tex]\( \boxed{1.37} \)[/tex], which corresponds to answer choice D.
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