Using logarithmic laws: log(a) + log(b) = log(ab)
log₄ (x + 9) + log₄ (x + 21) = log₄ [(x + 9)(x + 21)] = 3
Since we want the equation in terms of x, the next intuitive step is take 4 to the power of both sides, because the left hand side will simplify easily.
![4^{log_4 (x + 9)(x + 21)} = 4^{3}](https://tex.z-dn.net/?f=4%5E%7Blog_4%20%28x%20%2B%209%29%28x%20%2B%2021%29%7D%20%3D%204%5E%7B3%7D)
![(x + 9)(x + 21) = 64](https://tex.z-dn.net/?f=%28x%20%2B%209%29%28x%20%2B%2021%29%20%3D%2064)
![x^{2} + 9x + 21x + 189 = 64](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%209x%20%2B%2021x%20%2B%20189%20%3D%2064)
Solving the quadratic we get:
![x^{2} + 30x + 125 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%2030x%20%2B%20125%20%3D%200)
![(x + 5)(x + 25) = 0](https://tex.z-dn.net/?f=%28x%20%2B%205%29%28x%20%2B%2025%29%20%3D%200)
![x = -5, -25](https://tex.z-dn.net/?f=x%20%3D%20-5%2C%20-25)
BUT, for the logarithmic equation to be defined, x > -9, so x≠ -25
Thus, the only solution is x = -5.
Answer:
x =50
Step-by-step explanation:
Answer:
it's 3
Step-by-step explanation:
Number 3 is 3 units away from 0, and thus the absolute value of 3 is 3.
Answer:
please give me brainlist and follow
Step-by-step explanation:
42 ÷ w = 7 for w = 6. First, Shaylee must substitute ( ) for ( ). To simplify, Shaylee must divide ( ) by ( ) .