Please help with this Advanced Function math.

There are 13 questions, please don't write them on paper just write it below on a comment or use some software.

1. Fill in the table. [K2] Exponential Form Logarithmic Form 2401 = 74 a = log, c 2. Solve for x. Give answer to three decimal places where applicable. [K2] a. x = log 37 b. x = log 10 0003. Convert each of the following to exponential form and solve. [K6] a. n = log 16384 b. 6 = log 46656 4. Use the special properties of logarithms to solve the following equations. [K4] a. M = log, 1121 b. 410857 = x C. x = log,,785. Evaluate the following using a method of your choice. [A4] a. log,729 = b. log 7776- log, 36 = 6. Solve for the unknown variable using a method of your choice. [A4] [C2] a. 511x+23 = 1257x b. 2" = 123 7. Solve for the unknown variable using a method of your choice. [T4] [C2] 3x+5 + 3* = 177 8768. Describe the transformations on the given logarithmic function. [06] 800 = 10g10[_ %(x 7)] 85 9. Write the equation of a logarithmic function that has been vertically stretched by 5, reected in the x axis, horizontally compressed by 1/3, moved 11 units left and 8 units down. Justify your answer. [A5] [02] 10. The point ( 23, 13) is on the transformed function: y = 210gm[ 5(x + 3)] 9. Find the original point on the parent function f(x) = Iogmx. Justify your answer. [T4] [C2] 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. [T4] [C2] 12. The hydrogen ion concentration of a lemon is about 0.01. What is its pH? [A3] 13. How does an earthquake of magnitude 8.4 compare to an earthquake of magnitude 3.7? Round answer to the nearest whole number. [A4]