Answer To The Whole Assignment
1. x= 44
2. x=7
3. (in order first box to last) 2,5,1,4,3
4. x= -5
5. D. This number is a true solution of the original equation.
6. x=2
7. A. log2[x(x – 6)] = 4
8. C. x2 – 6x – 16 = 0
9. x=8
10. x=1, x=2
11. There is no solution.
12. x=3 or x=-3
13. C. Only –3 is an extraneous solution.
14. The bases of the logarithms are not the same.The one-to-one property does not apply when the bases are not the same.The change of base formula should have been used to write the logarithms with the same base.
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By using logarithmic properties, we will see that the solution is x = 44.
First, we need to remember 3 relations:
[tex]log_a(x) = ln(x)/ln(a)\\\\exp(ln(x)) = x\\\\ln(x^a) = a*ln(x)[/tex]
Now, our equation is:
[tex]log_4(x + 20) = 3[/tex]
Using the first relation, we get:
[tex]ln(x + 20)/ln(4) = 3\\\\ln(x + 20) = 3*ln(4)[/tex]
Using the third relation, we can rewrite:
[tex]ln(x + 20) = ln(4^3) = ln(64)[/tex]
Now if we use the second relation and apply the exponential function to both sides, we will get:
[tex]x + 20 = 64\\x = 64 - 20 = 44[/tex]
That is the solution to the equation.
If you want to learn more about logarithms, you can read:
https://brainly.com/question/13473114
