Answer:
![x = 4ln(12) = 9.94](https://tex.z-dn.net/?f=x%20%3D%204ln%2812%29%20%3D%209.94)
Step-by-step explanation:
We need to find the solution to the following equation:
. Given that the the natural logarithm is the inverse function of the exponential, we have that:
.
Applying this rule:
⇒ ![3x = ln(12)](https://tex.z-dn.net/?f=3x%20%3D%20ln%2812%29)
Solving for 'x':
⇒ ![x = 4ln(12)](https://tex.z-dn.net/?f=x%20%3D%204ln%2812%29)
With the help of a calculator: ![x = 4ln(12) = 9.94](https://tex.z-dn.net/?f=x%20%3D%204ln%2812%29%20%3D%209.94)
Answer:
x=2
Step-by-step explanation:
6x+11-4x=15
2x+11=15
2x=4
x=2
Answer:
Natalie cannot make it over the fence.
Step-by-step explanation:
After reading the statement, we must demostrate if the following inequation is possible, that is:
After some algebraic handling we find this equivalent expression:
(1)
The polynomial is factorized by the Quadratic Formula:
![\left(t-0.563-i\,0.348)\cdot (t-0.563+i\,0.348)\le 0](https://tex.z-dn.net/?f=%5Cleft%28t-0.563-i%5C%2C0.348%29%5Ccdot%20%28t-0.563%2Bi%5C%2C0.348%29%5Cle%200)
Since all roots are complex, we conclude that Natalie cannot make it over the fence.