Respuesta :
keep in mind that "ln" is just a shortcut for the logarithm with a base of "e".
[tex]\bf \textit{exponential form of a logarithm}\\\\ log_{{ a}}{{ ( b)}}=y \implies {{ a}}^y={{ b}}\qquad\qquad % exponential notation 2nd form {{ a}}^y={{ b}}\implies log_{{ a}}{{(b)}}=y \\\\ -------------------------------\\\\ e^{4x}=5\implies log_e(5)=4x\implies ln(5)=4x[/tex]
[tex]\bf \textit{exponential form of a logarithm}\\\\ log_{{ a}}{{ ( b)}}=y \implies {{ a}}^y={{ b}}\qquad\qquad % exponential notation 2nd form {{ a}}^y={{ b}}\implies log_{{ a}}{{(b)}}=y \\\\ -------------------------------\\\\ e^{4x}=5\implies log_e(5)=4x\implies ln(5)=4x[/tex]
Answer:
C) ln 5 = 4x is correct option .
Step-by-step explanation:
Given : [tex]e^{4x}[/tex] = 5
To find : Which logarithmic equation is equivalent to the exponential equation
Solution : We have given that [tex]e^{4x}[/tex] = 5.
By the exponential form of logarithm:
[tex]b^{a}[/tex] = c then logarithm form is [tex]log_{b} (c)[/tex]= a.
Then , [tex]e^{4x}[/tex] = 5 logarithm form is [tex]log_{e} (5)[/tex]= 4x.
Here, [tex]log_{e}[/tex] = ln
So, ln 5 = 4x.
Therefore , C) ln 5 = 4x is correct option .
