The value of x nearest to thousandths is 74.207
Solution:
Given that,
[tex]\text{ln } 2 + \text{ln } x = 5[/tex] ------ eqn 1
We can use logarithmic properties to solve for "x"
Using logarithmic properties:
[tex]\ln (mn) = \ln m + \ln n[/tex]
Therefore, apply the above property in eqn 1
[tex]\text{ln } 2 + \text{ln } x = 5\\\\\text{ln } 2x = 5[/tex]
By using the logarithmic property,
[tex]\text{If } \ln x = a , \text{ then } x = e^a[/tex]
Apply the above logarithmic property in above expression
[tex]\text{ln } 2x = 5\\\\2x = e^5[/tex]
Solve the above equation
We know that,
[tex]e^5 = 148.413159103[/tex]
[ use calculator ]
Therefore,
[tex]2x = 148.413159103\\\\x = \frac{148.413159103}{2}\\\\x = 74.2065795513\\\\x \approx 74.207[/tex]
Therefore, the value of x nearest to thousandths is 74.207
