Question

Which logarithmic equation is equivalent to the exponential equation below? e^4x = 5 (the x is part of the ^4 exponent) A. log 5 = 4x B. ln 4x = 5 C. ln 5 = 4x D. log 4x = 5

Answer 1

Keep in mind that "ln" is just a shortcut for the logarithm with a base of "e".

$\bf \textit{exponential form of a logarithm}\\\\ log_{{ a}}{{ ( b)}}=y \implies {{ a}}^y={{ b}}\qquad\qquad % exponential notation 2nd form {{ a}}^y={{ b}}\implies log_{{ a}}{{(b)}}=y \\\\ -------------------------------\\\\ e^{4x}=5\implies log_e(5)=4x\implies ln(5)=4x$

Answer 2

Answer:

C) ln 5 = 4x is correct option .

Step-by-step explanation:

Given : $e^{4x}$ = 5

To find : Which logarithmic equation is equivalent to the exponential equation

Solution : We have given that $e^{4x}$ = 5.

By the exponential form of logarithm:

$b^{a}$ = c then logarithm form is $log_{b} (c)$= a.

Then , $e^{4x}$ = 5  logarithm form is $log_{e} (5)$= 4x.

Here, $log_{e}$ = ln

So, ln 5 = 4x.

Therefore , C) ln 5 = 4x is correct option .