Solved on Feb 02, 2024

Find the value of $y$ given the equation $y = a + b \ln x$ , where $a = 50.0391615882$ , $b = 9.67624973418$ , and $x = 19$ .

STEP 1

Assumptions
1. The equation given is $y = a + b \ln x$
2. The value of $a$ is $50.0391615882$
3. The value of $b$ is $9.67624973418$
4. The value of $x$ is $19$
5. We need to find the value of $y$

STEP 2

First, we will substitute the given values of $a$ , $b$ , and $x$ into the equation.
$y = a + b \ln x$

STEP 3

Substitute $a = 50.0391615882$ , $b = 9.67624973418$ , and $x = 19$ into the equation.
$y = 50.0391615882 + 9.67624973418 \ln 19$

STEP 4

Now, we need to calculate the natural logarithm of $x$ , which is $\ln 19$ .

STEP 5

Use a calculator or a mathematical software to find $\ln 19$ .

STEP 6

After calculating $\ln 19$ , we get the following value (rounded to 10 decimal places):
$\ln 19 \approx 2.94443897917$

STEP 7

Now, multiply the value of $b$ by $\ln 19$ to get the second term of the equation.
$b \ln x = 9.67624973418 \times 2.94443897917$

STEP 8

Perform the multiplication to get the value of the second term.
$b \ln x \approx 9.67624973418 \times 2.94443897917 \approx 28.5045306543$

STEP 9

Now, add the value of $a$ to the result of $b \ln x$ to find $y$ .
$y = a + b \ln x$

STEP 10

Substitute the values of $a$ and $b \ln x$ into the equation.
$y = 50.0391615882 + 28.5045306543$

STEP 11

Add the two values to get the final value of $y$ .
$y \approx 50.0391615882 + 28.5045306543 \approx 78.5436922425$
The value of $y$ is approximately $78.5436922425$ .

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Find the value of $y$ given the equation $y = a + b \ln x$ , where $a = 50.0391615882$ , $b = 9.67624973418$ , and $x = 19$ .

STEP 1

Assumptions
1. The equation given is $y = a + b \ln x$
2. The value of $a$ is $50.0391615882$
3. The value of $b$ is $9.67624973418$
4. The value of $x$ is $19$
5. We need to find the value of $y$

STEP 2

First, we will substitute the given values of $a$ , $b$ , and $x$ into the equation.
$y = a + b \ln x$

STEP 3

Substitute $a = 50.0391615882$ , $b = 9.67624973418$ , and $x = 19$ into the equation.
$y = 50.0391615882 + 9.67624973418 \ln 19$

STEP 4

Now, we need to calculate the natural logarithm of $x$ , which is $\ln 19$ .

STEP 5

Use a calculator or a mathematical software to find $\ln 19$ .

STEP 6

After calculating $\ln 19$ , we get the following value (rounded to 10 decimal places):
$\ln 19 \approx 2.94443897917$

STEP 7

Now, multiply the value of $b$ by $\ln 19$ to get the second term of the equation.
$b \ln x = 9.67624973418 \times 2.94443897917$

STEP 8

Perform the multiplication to get the value of the second term.
$b \ln x \approx 9.67624973418 \times 2.94443897917 \approx 28.5045306543$

STEP 9

Now, add the value of $a$ to the result of $b \ln x$ to find $y$ .
$y = a + b \ln x$

STEP 10

Substitute the values of $a$ and $b \ln x$ into the equation.
$y = 50.0391615882 + 28.5045306543$

STEP 11

Add the two values to get the final value of $y$ .
$y \approx 50.0391615882 + 28.5045306543 \approx 78.5436922425$
The value of $y$ is approximately $78.5436922425$ .

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Find the value of yyy given the equation y=a+bln⁡xy = a + b \ln xy=a+blnx, where a=50.0391615882a = 50.0391615882a=50.0391615882, b=9.67624973418b = 9.67624973418b=9.67624973418, and x=19x = 19x=19.

STEP 1

Assumptions1. The equation given is y=a+bln⁡x y = a + b \ln x y=a+blnx2. The value of a a a is 50.0391615882 50.0391615882 50.03916158823. The value of b b b is 9.67624973418 9.67624973418 9.676249734184. The value of x x x is 19 19 195. We need to find the value of y y y

STEP 2

First, we will substitute the given values of a a a, b b b, and x x x into the equation.y=a+bln⁡x y = a + b \ln x y=a+blnx

STEP 3

Substitute a=50.0391615882 a = 50.0391615882 a=50.0391615882, b=9.67624973418 b = 9.67624973418 b=9.67624973418, and x=19 x = 19 x=19 into the equation.y=50.0391615882+9.67624973418ln⁡19 y = 50.0391615882 + 9.67624973418 \ln 19 y=50.0391615882+9.67624973418ln19

STEP 4

Now, we need to calculate the natural logarithm of x x x, which is ln⁡19 \ln 19 ln19.

STEP 5

Use a calculator or a mathematical software to find ln⁡19 \ln 19 ln19.

STEP 6

After calculating ln⁡19 \ln 19 ln19, we get the following value (rounded to 10 decimal places):ln⁡19≈2.94443897917 \ln 19 \approx 2.94443897917 ln19≈2.94443897917

STEP 7

Now, multiply the value of b b b by ln⁡19 \ln 19 ln19 to get the second term of the equation.bln⁡x=9.67624973418×2.94443897917 b \ln x = 9.67624973418 \times 2.94443897917 blnx=9.67624973418×2.94443897917

STEP 8

Perform the multiplication to get the value of the second term.bln⁡x≈9.67624973418×2.94443897917≈28.5045306543 b \ln x \approx 9.67624973418 \times 2.94443897917 \approx 28.5045306543 blnx≈9.67624973418×2.94443897917≈28.5045306543

STEP 9

Now, add the value of a a a to the result of bln⁡x b \ln x blnx to find y y y.y=a+bln⁡x y = a + b \ln x y=a+blnx

STEP 10

Substitute the values of a a a and bln⁡x b \ln x blnx into the equation.y=50.0391615882+28.5045306543 y = 50.0391615882 + 28.5045306543 y=50.0391615882+28.5045306543

STEP 11

Add the two values to get the final value of y y y.y≈50.0391615882+28.5045306543≈78.5436922425 y \approx 50.0391615882 + 28.5045306543 \approx 78.5436922425 y≈50.0391615882+28.5045306543≈78.5436922425The value of y y y is approximately 78.5436922425 78.5436922425 78.5436922425.

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Find the value of $y$ given the equation $y = a + b \ln x$ , where $a = 50.0391615882$ , $b = 9.67624973418$ , and $x = 19$ .

Assumptions
1. The equation given is $y = a + b \ln x$
2. The value of $a$ is $50.0391615882$
3. The value of $b$ is $9.67624973418$
4. The value of $x$ is $19$
5. We need to find the value of $y$

First, we will substitute the given values of $a$ , $b$ , and $x$ into the equation.
$y = a + b \ln x$

Substitute $a = 50.0391615882$ , $b = 9.67624973418$ , and $x = 19$ into the equation.
$y = 50.0391615882 + 9.67624973418 \ln 19$

Now, we need to calculate the natural logarithm of $x$ , which is $\ln 19$ .

Use a calculator or a mathematical software to find $\ln 19$ .

After calculating $\ln 19$ , we get the following value (rounded to 10 decimal places):
$\ln 19 \approx 2.94443897917$

Now, multiply the value of $b$ by $\ln 19$ to get the second term of the equation.
$b \ln x = 9.67624973418 \times 2.94443897917$

Perform the multiplication to get the value of the second term.
$b \ln x \approx 9.67624973418 \times 2.94443897917 \approx 28.5045306543$

Now, add the value of $a$ to the result of $b \ln x$ to find $y$ .
$y = a + b \ln x$

Substitute the values of $a$ and $b \ln x$ into the equation.
$y = 50.0391615882 + 28.5045306543$

Add the two values to get the final value of $y$ .
$y \approx 50.0391615882 + 28.5045306543 \approx 78.5436922425$
The value of $y$ is approximately $78.5436922425$ .