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

C) ln 5 = 4x is correct option .

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 .