i send u a picture of how i solve it. i hope this can help u
Step-by-step explanation:
2^(2x) - 5(2^x) = -4
(2^x)^2 - 5(2^x) = -4
Substitute 2^x = z --> x = ln(z)/ln(2)
z^2 - 5z = -4
z^2 - 5z + 4 = 0
(z - 1)(z - 4) = 0
z = 1 --> x = ln(1)/ln(2) = 0
z = 4 --> x = ln(4)/ln(2) = 2
Answer:
The equation of the line in slope-intercept form is:
Step-by-step explanation:
Given the points
Finding the slope
![\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(-8,\:5\right),\:\left(x_2,\:y_2\right)=\left(-1,\:-5\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%28-8%2C%5C%3A5%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%28-1%2C%5C%3A-5%5Cright%29)
![m=\frac{-5-5}{-1-\left(-8\right)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-5-5%7D%7B-1-%5Cleft%28-8%5Cright%29%7D)
![m=-\frac{10}{7}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B10%7D%7B7%7D)
We know the slope-intercept form of the line equation is
![y = mx+b](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
where m is the slope and b is the y-intercept
substituting m = -10/7 and (-8, 5) in the slope-intercept form to determine the y-intercept
![5\:=\:\frac{-10}{7}\left(-8\right)+b](https://tex.z-dn.net/?f=5%5C%3A%3D%5C%3A%5Cfrac%7B-10%7D%7B7%7D%5Cleft%28-8%5Cright%29%2Bb)
![\frac{80}{7}+b=5](https://tex.z-dn.net/?f=%5Cfrac%7B80%7D%7B7%7D%2Bb%3D5)
![b=-\frac{45}{7}](https://tex.z-dn.net/?f=b%3D-%5Cfrac%7B45%7D%7B7%7D)
now substituting m = -10/7 and b = -45/7 in the slope-intercept form
![y = mx+b](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
![y\:=\:\frac{-10}{7}x+\left(-\frac{45}{7}\right)](https://tex.z-dn.net/?f=y%5C%3A%3D%5C%3A%5Cfrac%7B-10%7D%7B7%7Dx%2B%5Cleft%28-%5Cfrac%7B45%7D%7B7%7D%5Cright%29)
![y\:=\:\frac{-10}{7}x-\frac{45}{7}](https://tex.z-dn.net/?f=y%5C%3A%3D%5C%3A%5Cfrac%7B-10%7D%7B7%7Dx-%5Cfrac%7B45%7D%7B7%7D)
Thus, the equation of the line in slope-intercept form is:
Step-by-step explanation:
Hope this helps, happy studying!