Answer :
Let's solve the equation [tex]\( 7 \cdot \ln(x) = 2.4 \)[/tex] step by step.
1. Isolate the natural logarithm term:
Divide both sides of the equation by 7 to isolate [tex]\( \ln(x) \)[/tex].
[tex]\[ \ln(x) = \frac{2.4}{7} \][/tex]
Calculating the right-hand side:
[tex]\[ \ln(x) = 0.34285714285714286 \][/tex]
2. Solve for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], we need to exponentiate both sides using the base [tex]\( e \)[/tex] (where [tex]\( e \approx 2.71828 \)[/tex]):
[tex]\[ x = e^{0.34285714285714286} \][/tex]
Doing this calculation:
[tex]\[ x \approx 1.4089674664819067 \][/tex]
3. Round the answer:
Finally, round the answer to two decimal places:
[tex]\[ x \approx 1.41 \][/tex]
Thus, the solution to the equation [tex]\( 7 \cdot \ln(x) = 2.4 \)[/tex] rounded to two decimal places is:
[tex]\[ \boxed{x = 1.41} \][/tex]
So, the correct answer is B. [tex]\( x = 1.41 \)[/tex].
1. Isolate the natural logarithm term:
Divide both sides of the equation by 7 to isolate [tex]\( \ln(x) \)[/tex].
[tex]\[ \ln(x) = \frac{2.4}{7} \][/tex]
Calculating the right-hand side:
[tex]\[ \ln(x) = 0.34285714285714286 \][/tex]
2. Solve for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], we need to exponentiate both sides using the base [tex]\( e \)[/tex] (where [tex]\( e \approx 2.71828 \)[/tex]):
[tex]\[ x = e^{0.34285714285714286} \][/tex]
Doing this calculation:
[tex]\[ x \approx 1.4089674664819067 \][/tex]
3. Round the answer:
Finally, round the answer to two decimal places:
[tex]\[ x \approx 1.41 \][/tex]
Thus, the solution to the equation [tex]\( 7 \cdot \ln(x) = 2.4 \)[/tex] rounded to two decimal places is:
[tex]\[ \boxed{x = 1.41} \][/tex]
So, the correct answer is B. [tex]\( x = 1.41 \)[/tex].
