Question

Rewrite this exponential equation as a logarithmic equation. 4e^x=16

Answer 1

Answer:

The rewritten equation is: $x = \ln{4}$

Step-by-step explanation:

The inverse operation of the exponential is the natural logarithm, $\ln$, and the following property is used to solve this question:

$\ln{e^x} = x$

In this question, we have that:

$4e^x = 16$

$e^x = \frac{16}{4}$

$e^x = 4$

Applying the natural logarithm to both sides:

$\ln{e^x} = \ln{4}$

$x = \ln{4}$

The rewritten equation is: $x = \ln{4}$

Answer 2

The equivalent logarithmic equation is: $x = \log(4)$

The exponential equation is given as:

$4e^x=16$

Divide both sides of the equation by 4

$e^x=4$

Next, take the logarithm of both sides (to convert the expression to a logarithmic expression)

$\log(e^x)=\log(4)$

The logarithm of e^x is x.

So, we have:

$x = \log(4)$

Hence, the equivalent logarithmic equation is: $x = \log(4)$

Read more about equivalent equation at:

https://brainly.com/question/6841768