or screenshot in your solution.12. Why must the base of a logarithm be positive?13. Why can we not calculate the logarithm of a negative number?14. Rod says that he is thinking of a one variable exponential or logarithmic equation thathas the following characteristics:a. has solutions x 1 and x = 2b. does not contain the digit "3"c. contains the number -12.What are two different equations that Rod could be thinking of? Are those the onlypossible answers?15. Solve, rounding final answers to three decimals where appropriate, = 2(6x²-²)5x√516. Solve, rounding to three decimals where appropriate, logx-4(3x + 1) = 2 1. Convert the following expressions between exponential and logarithmic form.a. 2401 = 74b.= logb cCa.b.a =2. Solve for x. Give your answer to three decimal places where appropriate.x = log 21x = log22 10 000C.2x = 23d. x⁹ = 1024e.5 = logx 25f. 3.5 = log36 X3. Use the properties of logarithms to solve the following equations.a. M = log₁1 (11²¹)b. 4log4 (57) = XC. X = log100 10004. Solve for the unknown using a method of your choice.a. 511x+23 1257xb. 22 123C. 3x+5 + 3x = 177876=-log[(x − 2)] ₁5. Describe the transformations on the logarithmic function g(x) = -+96. Write the equation of a logarithmic function that has been vertically stretched by 4,reflected in the x-axis, horizontally compressed by 1/9, moved 11 units up and 12 unitsleft. Justify your answer.7. Ethan bought a new car worth $54,000. After 5 years, the car was worth $28,497.52.Calculate the annual depreciation rate of Ethan's car.8. The hydrogen ion concentration of a lemon is about 0.02. What is its pH?9. How do the intensities of a magnitude 6.0 earthquake and a magnitude 2.9 earthquakecompare?10. Using logarithm properties there are multiple ways of expressing the sametransformations on a parent function. Given g(x) = 8 log[2(x)], find equivalent functionsin the following forms. Round values to 4 decimal places where appropriate.a. g(x) = log(x) + cb. g(x) = logb[k(x)]c. g(x) = log[k (x)]11. Not all logarithmic and exponential equations can be solved algebraically. Usetechnology to solve the equation 32x-³ = log₂ (2x) to 4 decimal places. Include a sketch

Question

or screenshot in your solution.12. Why must the base of a logarithm be positive?13. Why can we not calculate the logarithm of a negative number?14. Rod says that he is thinking of a one variable exponential or logarithmic equation thathas the following characteristics:a. has solutions x 1 and x = 2b. does not contain the digit &#34;3&#34;c. contains the number -12.What are two different equations that Rod could be thinking of? Are those the onlypossible answers?15. Solve, rounding final answers to three decimals where appropriate, = 2(6x²-²)5x√516. Solve, rounding to three decimals where appropriate, logx-4(3x + 1) = 2 1. Convert the following expressions between exponential and logarithmic form.a. 2401 = 74b.= logb cCa.b.a =2. Solve for x. Give your answer to three decimal places where appropriate.x = log 21x = log22 10 000C.2x = 23d. x⁹ = 1024e.5 = logx 25f. 3.5 = log36 X3. Use the properties of logarithms to solve the following equations.a. M = log₁1 (11²¹)b. 4log4 (57) = XC. X = log100 10004. Solve for the unknown using a method of your choice.a. 511x+23 1257xb. 22 123C. 3x+5 + 3x = 177876=-log[(x − 2)] ₁5. Describe the transformations on the logarithmic function g(x) = -+96. Write the equation of a logarithmic function that has been vertically stretched by 4,reflected in the x-axis, horizontally compressed by 1/9, moved 11 units up and 12 unitsleft. Justify your answer.7. Ethan bought a new car worth $54,000. After 5 years, the car was worth $28,497.52.Calculate the annual depreciation rate of Ethan's car.8. The hydrogen ion concentration of a lemon is about 0.02. What is its pH?9. How do the intensities of a magnitude 6.0 earthquake and a magnitude 2.9 earthquakecompare?10. Using logarithm properties there are multiple ways of expressing the sametransformations on a parent function. Given g(x) = 8 log[2(x)], find equivalent functionsin the following forms. Round values to 4 decimal places where appropriate.a. g(x) = log(x) + cb. g(x) = logb[k(x)]c. g(x) = log[k (x)]11. Not all logarithmic and exponential equations can be solved algebraically. Usetechnology to solve the equation 32x-³ = log₂ (2x) to 4 decimal places. Include a sketch

Accepted Answer

1) We have to convert the following expressions between exponential and logarithm function.
(a)…

1. Convert the following expressions between exponential and logarithmic form. a. 2401 = 74 b. a = logb c