Option A :
is the solution of the equation.
Explanation:
The equation is ![$5+8 \ln x=15.8$](https://tex.z-dn.net/?f=%245%2B8%20%5Cln%20x%3D15.8%24)
To determine the value of x, let us simplify the equation.
Subtracting 5 from both sides of the equation, we have,
![$5+\ 8 \ ln \ x-5=15.8-5$](https://tex.z-dn.net/?f=%245%2B%5C%208%20%20%5C%20ln%20%5C%20x-5%3D15.8-5%24)
Simplifying, we get,
![8 \ ln \ x= 10.8](https://tex.z-dn.net/?f=8%20%5C%20ln%20%5C%20x%3D%2010.8)
Now , dividing both sides of the equation by 8, we get,
![$\ ln \ x=1.35$](https://tex.z-dn.net/?f=%24%5C%20ln%20%5C%20x%3D1.35%24)
Using the logarithmic definition that if
then ![$b=a^{c}$](https://tex.z-dn.net/?f=%24b%3Da%5E%7Bc%7D%24)
Thus, rewriting the above expression
using the logarithmic definition, we have,
⇒ ![$x=e^{1.35}$](https://tex.z-dn.net/?f=%24x%3De%5E%7B1.35%7D%24)
Substituting the value of
, we get,
![$x=3.85742 \ldots$](https://tex.z-dn.net/?f=%24x%3D3.85742%20%5Cldots%24)
Rounding off the answer to two decimal places, we get,
![$x=3.86$](https://tex.z-dn.net/?f=%24x%3D3.86%24)
Hence, the solution of the equation is ![$x=3.86$](https://tex.z-dn.net/?f=%24x%3D3.86%24)
Therefore, Option A is the correct answer.