Question

I have a question about a logarithmic equation I will upload a photo

Answer 1

To solve the solution of the exponential as shown below:

`5e^x-10=4`
`\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}`
`\begin{gathered} 5e^x=14 \\ (5e^x)/(5)=(14)/(5) \\ e^x=(14)/(5) \\ \text{applying exponential rule} \\ \text{ }\ln e^x=\ln ((14)/(5)) \\ x=\ln ((14)/(5)) \end{gathered}`

(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)