Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
To find the value of [tex]\( x \)[/tex] in the equation [tex]\( 19 + 2 \ln x = 25 \)[/tex], follow these steps:
1. Isolate the logarithmic term:
[tex]\[ 19 + 2 \ln x = 25 \][/tex]
First, subtract 19 from both sides to move 19 to the other side of the equation:
[tex]\[ 2 \ln x = 25 - 19 \][/tex]
Simplifying the right side gives:
[tex]\[ 2 \ln x = 6 \][/tex]
2. Solve for the natural logarithm:
Divide both sides by 2 to isolate [tex]\( \ln x \)[/tex]:
[tex]\[ \ln x = \frac{6}{2} \][/tex]
Simplifying gives:
[tex]\[ \ln x = 3 \][/tex]
3. Exponentiate to remove the natural logarithm:
Recall that [tex]\( \ln x \)[/tex] is the natural logarithm, which has the base [tex]\( e \)[/tex]. To solve for [tex]\( x \)[/tex], exponentiate both sides with base [tex]\( e \)[/tex]:
[tex]\[ x = e^3 \][/tex]
4. Calculate the numerical value:
The value of [tex]\( e^3 \)[/tex] is approximately:
[tex]\[ 20.085536923187668 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] that solves the equation [tex]\( 19 + 2 \ln x = 25 \)[/tex] is closest to:
D. 20.09
1. Isolate the logarithmic term:
[tex]\[ 19 + 2 \ln x = 25 \][/tex]
First, subtract 19 from both sides to move 19 to the other side of the equation:
[tex]\[ 2 \ln x = 25 - 19 \][/tex]
Simplifying the right side gives:
[tex]\[ 2 \ln x = 6 \][/tex]
2. Solve for the natural logarithm:
Divide both sides by 2 to isolate [tex]\( \ln x \)[/tex]:
[tex]\[ \ln x = \frac{6}{2} \][/tex]
Simplifying gives:
[tex]\[ \ln x = 3 \][/tex]
3. Exponentiate to remove the natural logarithm:
Recall that [tex]\( \ln x \)[/tex] is the natural logarithm, which has the base [tex]\( e \)[/tex]. To solve for [tex]\( x \)[/tex], exponentiate both sides with base [tex]\( e \)[/tex]:
[tex]\[ x = e^3 \][/tex]
4. Calculate the numerical value:
The value of [tex]\( e^3 \)[/tex] is approximately:
[tex]\[ 20.085536923187668 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] that solves the equation [tex]\( 19 + 2 \ln x = 25 \)[/tex] is closest to:
D. 20.09
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
it takes 10 workers 10 days to paint 10 houses. How many houses can five workers paint in five days?