Option A : [tex]$x=3.86$[/tex] is the solution of the equation.
Explanation:
The equation is [tex]$5+8 \ln x=15.8$[/tex]
To determine the value of x, let us simplify the equation.
Subtracting 5 from both sides of the equation, we have,
[tex]$5+\ 8 \ ln \ x-5=15.8-5$[/tex]
Simplifying, we get,
[tex]8 \ ln \ x= 10.8[/tex]
Now , dividing both sides of the equation by 8, we get,
[tex]$\ ln \ x=1.35$[/tex]
Using the logarithmic definition that if [tex]$\log _{a}(b)=c$[/tex] then [tex]$b=a^{c}$[/tex]
Thus, rewriting the above expression [tex]$\ ln \ x=1.35$[/tex] using the logarithmic definition, we have,
[tex]$\ln \ x =1.35$[/tex] ⇒ [tex]$x=e^{1.35}$[/tex]
Substituting the value of [tex]e^{1.35}$=3.85742...[/tex] , we get,
[tex]$x=3.85742 \ldots$[/tex]
Rounding off the answer to two decimal places, we get,
[tex]$x=3.86$[/tex]
Hence, the solution of the equation is [tex]$x=3.86$[/tex]
Therefore, Option A is the correct answer.