(15 pts)    1.     Solve the following equations algebraically for x (no calculators):
                        a.     x = log₂₅ 5          b.     x = 3 ln e⁴                 c.     10^{4 log x} = 16

(10 pts)     2.     Write each equation in exponential form:
                        a.     log ₄ 64 = 3                     b.     log _x 0.2 = -3

(20 pts)     3.     Use your calculator to compute x to four (4) decimal places:
                        a.     x = ln (7.39 + e ^2.34)         b.     x = log₁₃ 9

(10 pts)     4.     Solve algebraically for x: 3^x+3 + 3^x = 84

(15 pts)     5.     A bacteria culture doubles in size every 24 hours. Find how long it will take to triple its size, using the exponential growth model

(15 pts)     6.     A single deposit of $1000 compounded quarterly to $1205.18 after five years. Find the interest rate.

(15 pts)     7.     The management at a certain factory has found that the maximum number of items a worker can make per day is 30.   The learning curve for the number of units a new employee can make after t days is given by    N = 30(1 - e^kt).   After 20 days on the job a new employee makes 19 items in a day. Find how many more days it will take until this employee can make 25 items in a day.