Question

Let's solve the exponential equation 4ex = 80. (a) First, we isolate ex to get the equivalent equation Correct: Your answer is correct. . (b) Next, we take ln of each side to get the equivalent equation Incorrect: Your answer is incorrect. . (c) Now we use a calculator to find x ≈ 2.996 Correct: Your answer is correct. . (Round your answer to three decimal places.)

Answer 1

Answer:

The solution of the exponential equation $4e^{x} = 80$ is

x = 2.996

Step-by-step explanation:

To solve the exponential equation $4e^{x} = 80$

First, we will isolate $e^{x}$ by dividing both sides of the equation by 4, so that we get

$\frac{4e^{x}}{4} = \frac{80}{4}$

$e^{x} = 20$

Now, we will take the ln of both sides of the equation to get

$ln(e^{x}) =ln(20)$

(NOTE: $ln(e^{x}) = x$ )

Then,

$x =ln(20)$

$x = 2.9957$

∴ x = 2.996 (to three decimal places)

Hence, the solution of the exponential equation $4e^{x} = 80$ is

x = 2.996