To solve the solution of the exponential as shown below:
[tex]5e^x-10=4[/tex][tex]\begin{gathered} 5e^x-10=4 \\ \text{add 10 to both side } \\ 5e^x-10+10=4+10 \\ simplify \\ 5e^x=14 \\ \text{divide both side by 5} \end{gathered}[/tex][tex]\begin{gathered} 5e^x=14 \\ \frac{5e^x}{5}=\frac{14}{5} \\ e^x=\frac{14}{5} \\ \text{applying exponential rule} \\ \text{ }\ln e^x=\ln (\frac{14}{5}) \\ x=\ln (\frac{14}{5}) \end{gathered}[/tex]
(a) The exact solution, in terms of natural logarithm is: x = In (14/5)
(b) The appropriate solution, of x = 1.02961
Hence the value of x = 1.0296 (4dp)
