Assignment:
Use the algebraic definition of the logarithm to evaluate (simplify) the expression by hand and state the property number used. All work must be shown.
Q1. log8 (8^(x-1)
Q2. log4 ((1/16)^7)
Q3. log (0.0001)
Solve for x exactly by hand.
Q4. log5 (x - 1) = 1
Q5. log2 (1/8) = x
Q6. log7 (1) = x - 2
Simplify the following expressions completely using properties of logarithms. Keep all work on a line-by-line basis.
Q7. (3/2)log5(t6) - 2log5(t1/2) + 3log5(3) - (1/2)log5(81)
Q8. (20)log3(x1/4) - (2)log3(y) + (3)log3(y2/3) - (5/4)log3(x4)
Solve the exponential equations. Obtain both an exact and approximate value. As a reminder, do not use your calculator until you have algebraically solved for x. Include and distinguish both exact and approximate values.
Q9. (5)e(3t - 1) = 85
Q10. (2)3x - 7 = 11
Q11. A company manufacturing surfboards has fixed costs of $300 per day and total costs of $5,100 per day at a daily output of 20 boards.
a) Assuming that the total cost per day, , is linearly related to the total output per day, x, write an expression for the cost function.
b) The average cost per board for an output of x boards is given by . Find the average cost function.
c) On your own, graph the average cost function on your calculator for Do NOT include the graph here.
d) What does the average cost per board tend to as production increases? Briefly justify your answer using complete sentence(s).
Q12. a) Find a logarithmic regression model y=a+b ln(x) for the Total Production.
b) Calculate to the nearest million, the production in 2010. (Show the steps for evaluating the model for a given value x.)
Provide complete and step by step solution for the question and show calculations and use formulas.