This is the answer -1/6, -3, 1/6, .5,
For this case we must find an expression equivalent to:
![log_ {5} (\frac {x} {4}) ^ 2](https://tex.z-dn.net/?f=log_%20%7B5%7D%20%28%5Cfrac%20%7Bx%7D%20%7B4%7D%29%20%5E%202)
So:
We expanded
by moving 2 out of the logarithm:
![2log_ {5} (\frac {x} {4})](https://tex.z-dn.net/?f=2log_%20%7B5%7D%20%28%5Cfrac%20%7Bx%7D%20%7B4%7D%29)
By definition of logarithm properties we have to:
The logarithm of a product is equal to the sum of the logarithms of each factor:
![log (xy) = log (x) + log (y)](https://tex.z-dn.net/?f=log%20%28xy%29%20%3D%20log%20%28x%29%20%2B%20log%20%28y%29)
The logarithm of a division is equal to the difference of logarithms of the numerator and denominator.
![log (\frac {x} {y}) = log (x) -log (y)](https://tex.z-dn.net/?f=log%20%28%5Cfrac%20%7Bx%7D%20%7By%7D%29%20%3D%20log%20%28x%29%20-log%20%28y%29)
Then, rewriting the expression:
![2 (log_ {5} (x) -log_ {5} (4))](https://tex.z-dn.net/?f=2%20%28log_%20%7B5%7D%20%28x%29%20-log_%20%7B5%7D%20%284%29%29)
We apply distributive property:
![2log_ {5} (x) -2log_ {5} (4)](https://tex.z-dn.net/?f=2log_%20%7B5%7D%20%28x%29%20-2log_%20%7B5%7D%20%284%29)
Answer:
An equivalent expression is:
![2log_ {5} (x) -2log_ {5} (4)](https://tex.z-dn.net/?f=2log_%20%7B5%7D%20%28x%29%20-2log_%20%7B5%7D%20%284%29)
Answer:
![\tt C) \:\tt f^{-1}(x)=\cfrac{x-6}{3}](https://tex.z-dn.net/?f=%5Ctt%20C%29%20%5C%3A%5Ctt%20f%5E%7B-1%7D%28x%29%3D%5Ccfrac%7Bx-6%7D%7B3%7D)
Step-by-step explanation:
We're given,
![\tt f(x) = 3x + 6](https://tex.z-dn.net/?f=%5Ctt%20f%28x%29%20%3D%203x%20%2B%206)
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![\tt y=3x+6](https://tex.z-dn.net/?f=%5Ctt%20y%3D3x%2B6)
![\tt x=3y+6](https://tex.z-dn.net/?f=%5Ctt%20x%3D3y%2B6)
![\tt x-6=3y](https://tex.z-dn.net/?f=%5Ctt%20x-6%3D3y)
![\tt y=\cfrac{x-6}{3}](https://tex.z-dn.net/?f=%5Ctt%20y%3D%5Ccfrac%7Bx-6%7D%7B3%7D)
![\tt f^{-1}(x)=\cfrac{x-6}{3}](https://tex.z-dn.net/?f=%5Ctt%20f%5E%7B-1%7D%28x%29%3D%5Ccfrac%7Bx-6%7D%7B3%7D)
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Answer:
thr answers are A and D of the question