The solution of the exponential function is option (C) [tex]x=\frac{ln3}{2}[/tex] is the correct answer.
What is of natural log function?
The natural log is the logarithm to the base of the number e and is the inverse function of an exponential function. It is denoted by ln x.
For the given situation,
The function is 5e^2x - 4 = 11
⇒ [tex]5e^{2x} - 4 = 11[/tex]
⇒ [tex]5e^{2x} = 11+4[/tex]
⇒ [tex]5e^{2x} = 15[/tex]
⇒ [tex]e^{2x} = \frac{15}{5}[/tex]
⇒ [tex]e^{2x} = 3[/tex]
Taking ln on both sides,
⇒ [tex]ln e^{2x} = ln3[/tex] [∵ ln e = 1 ]
⇒ [tex]{2x} = ln3[/tex]
⇒ [tex]x=\frac{ln3}{2}[/tex]
Hence we can conclude that the solution of the exponential function is option (C) [tex]x=\frac{ln3}{2}[/tex] is the correct answer.
Learn more about natural log function here
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