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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. 

**** all answers were found off of brainly.com *******

facundo3141592

By using logarithmic properties, we will see that the solution is x = 44.

How to solve logarithmic equations?

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

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