Answer:
x = -2
Step-by-step explanation:
We are given the logarithmic base 2 equation of:
![\displaystyle{\log_2 (4x) + \log_2 (x+1) = 3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Clog_2%20%284x%29%20%2B%20%5Clog_2%20%28x%2B1%29%20%3D%203%7D)
Apply logarithm property of addition where:
![\displaystyle{\log_a M + \log_a N = \log_a MN}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Clog_a%20M%20%2B%20%5Clog_a%20N%20%3D%20%5Clog_a%20MN%7D)
Therefore, we will write new equation as:
![\displaystyle{\log_2 [4x(x+1)] = 3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Clog_2%20%5B4x%28x%2B1%29%5D%20%3D%203%7D)
Apply logarithm to exponential form using:
![\displaystyle{\log_a M = N \to a^N = M}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Clog_a%20M%20%3D%20N%20%5Cto%20a%5EN%20%3D%20M%7D)
Thus, another new rewritten equation is:
![\displaystyle{2^3 = 4x(x+1)}\\\\\displaystyle{8 = 4x(x+1)}\\\\\displaystyle{2=x(x+1)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B2%5E3%20%3D%204x%28x%2B1%29%7D%5C%5C%5C%5C%5Cdisplaystyle%7B8%20%3D%204x%28x%2B1%29%7D%5C%5C%5C%5C%5Cdisplaystyle%7B2%3Dx%28x%2B1%29%7D)
Expand the expression in and arrange the terms in quadratic expression:
![\displaystyle{2=x^2+x}\\\\\displaystyle{0=x^2+x-2}\\\\\displaystyle{x^2+x-2=0}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B2%3Dx%5E2%2Bx%7D%5C%5C%5C%5C%5Cdisplaystyle%7B0%3Dx%5E2%2Bx-2%7D%5C%5C%5C%5C%5Cdisplaystyle%7Bx%5E2%2Bx-2%3D0%7D)
Solve for x:
![\displaystyle{(x+2)(x-1)=0}\\\\\displaystyle{x=-2,1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%28x%2B2%29%28x-1%29%3D0%7D%5C%5C%5C%5C%5Cdisplaystyle%7Bx%3D-2%2C1%7D)
These are potential solutions to the equation. To find extraneous solution, you’ll have to know the domain of logarithm function. We know that logarithm’s domain is defined to be greater than 0. Henceforth, anti-logarithm must be greater than 0.
( 1 ) 4x > 0, x > 0
( 2 ) x + 1 > 0, x > -1
Therefore, our anti-log must be greater than 0, so any solutions that are equal or less than 0 will be considered as extraneous solution.
Hence, x = -2 is the extraneous solution.
Answer: It is A.
Step-by-step explanation:
if you plug 0 into h(x) you will get a negative number under the square root, which makes it an imaginary number. w(x) is self explanatoru
B. is the answer.
If the sum of 10 and another product of 7 than the answer is B.
Answer:
7p+4
Step-by-step explanation:
i think it is that becasue the negative sign in front of -5 cancels out the negative and now u have poisitive 5. Subract 1 from it and you get 4. Thus, the answers is 7p+4
Hope it helps!
-Angel Kraft