Help Solve:

1. 4^x= 64

2. log₄(64)

3. y = e³

4. log(x) + log(x) = 2

5. 2log(x) - log(x²) + log(2/x) + log(x)

6. Evaluate log₃(45)

7.log₄(x²) - log₄(4x - 4) = 0

8. log₂(x) + log₂(x + 2) = 3

9. 2^{(2x + 2)}= 64

10. 3^{(x2+ 2x)}= 27

11. 4^x= 63

12. 10^4x= 101

13. Expand the following

Log ( (x²+ 6x + 9) / (x²-9) )

14. Create an equivalent logarithimic equation for 6^x= 12

15. Create an equivalent logarithimic equation for x⁷= 15

16. 4^{(x + 2)}= 200

17. The hydrogen ion concentration of a dilute solution of an acid is measured to be [H+] = 2.0 x 10^(-4). Determine the pH of the solution.

18. After 5 hours an initial bacteria population of 100 members has increased in size to 500 members. Determine the exponential growth rate of the colony of bacteria.

19.What can you say about the function graphed here?Explain yourreasoning:Is it a log or an exponential?For an exponential, isthe exponent x or -x?What is the equation of the asymptote?Which direction and how many units is it shifted?

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