Solved on Feb 02, 2024

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

STEP 1

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

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

After calculating ln19 \ln 19 , we get the following value (rounded to 10 decimal places):
ln192.94443897917 \ln 19 \approx 2.94443897917

STEP 7

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

STEP 8

Perform the multiplication to get the value of the second term.
blnx9.67624973418×2.9444389791728.5045306543 b \ln x \approx 9.67624973418 \times 2.94443897917 \approx 28.5045306543

STEP 9

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

STEP 10

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

STEP 11

Add the two values to get the final value of y y .
y50.0391615882+28.504530654378.5436922425 y \approx 50.0391615882 + 28.5045306543 \approx 78.5436922425
The value of y y is approximately 78.5436922425 78.5436922425 .

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