Question

Solve the equation log4(x + 20) = 3

Answer 1

Answer:

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. 

Answer 2

Answer:

Step-by-step explanation:

I don not understand what is for 4 here. So there are 2 cases:

Case 1: If you mean: log[4(x+20)]= 3

We know 3 = log(10^3)= log(1000)

So we have log[4(x+20)]= log(1000)

so 4(x+20)= 1000

and x+20 = 1000/4

x+20 = 250 and finally x= 250-20, x=230

The solution is 230.

Case 2; If you mean that 4 is the base of logarithm.

$log_{4}(x+20)= 3$

and we know that $3=log_{4}(3^{4} )= log_{4}(81)$

So we have $log_{4}(x+20)= log_{4}(81)$

and x+20 = 81

or x= 81-20

x=61

The answer is 61.

Hope that useful for you, both cases.