1.Fill in the table

Exponential Form: 2401 = 7⁴ , Logarithmic Form: ?

Logarithmic Form:a = log_bc , Exponential Form: ?

2.Solve for x. Give answer to three decimal places where applicable.

a. x=log37

b. x=log10000

3.Convert each of the following to exponential form and solve.

a. n = log₄16384

b.6 = log_b46656

4.Use the special properties of logarithms to solve the following equations.

a. M = log₁₁11²¹

b. 4^log₄⁵⁷ = x

c. x=log₂₃78

5. Evaluate the following using a method of your choice.

a. log₉729 =

b. log₆7776 log₆36 =

6. Solve for the unknown variable using a method of your choice.

a. 5^{11x+ 23} = 125^7x

b. 2ⁿ = 123

7. Solve for the unknown variable using a method of your choice.

3^{x+ 5} + 3^x = 177876

8. Describe the transformations on the given logarithmic function.

g(x) = 1/6 log₁₀[ 1/6(x 7)] 85

9. Write the equation of a logarithmic function that has been vertically stretched by 5, reflected in the xaxis, horizontally compressed by 1/3, moved 11 units left and 8 units down. Justify your answer.

10. The point ( 23, 13) is on the transformed function: y = 2log₁₀[ 5(x + 3)]9. Find the original point on the parent function f(x)=log₁₀x. Justify your answer.

11.Ethan bought new car worth $60 000. After 5 years, the car was worth $35,429.40. Calculate the depreciation rate of the Ethan's car.

12.The hydrogen ion concentration of a lemon is about 0.01. What is its pH?

13. How does an earthquake of magnitude 8.4 compare to an earthquake of magnitude 3.7? Round answer to the nearest whole number.