Answer:
The solution of the exponential equation [tex]4e^{x} = 80[/tex] is
x = 2.996
Step-by-step explanation:
To solve the exponential equation [tex]4e^{x} = 80[/tex]
First, we will isolate [tex]e^{x}[/tex] by dividing both sides of the equation by 4, so that we get
[tex]\frac{4e^{x}}{4} = \frac{80}{4}[/tex]
[tex]e^{x} = 20[/tex]
Now, we will take the ln of both sides of the equation to get
[tex]ln(e^{x}) =ln(20)[/tex]
(NOTE: [tex]ln(e^{x}) = x[/tex] )
Then,
[tex]x =ln(20)[/tex]
[tex]x = 2.9957[/tex]
∴ x = 2.996 (to three decimal places)
Hence, the solution of the exponential equation [tex]4e^{x} = 80[/tex] is
x = 2.996
Exponential equations are represents as: [tex]\mathbf{ae^x = n}[/tex]
The approximated value of x is 2.996
The equation is given as:
[tex]\mathbf{4e^x = 80}[/tex]
(a) Isolate e^x
To do this, we divide both sides by 4
[tex]\mathbf{e^x = 20}[/tex]
(b) Take ln of both sides
This given
[tex]\mathbf{ln(e^x) = ln(20)}[/tex]
This gives
[tex]\mathbf{x = ln(20)}[/tex]
(c) Using a calculator
Using a calculator, we have:
[tex]\mathbf{ ln(20) \approx 2.996}[/tex]
So, we have:
[tex]\mathbf{ x \approx 2.996}[/tex]
Hence, the approximated value of x is 2.996
Read more about exponential equations at:
https://brainly.com/question/11672641
