1. What are (a) log(1000) (d) log(10*) (b) log(0.01) (e) In(ekt) (c) log(-10) (f) log2(16) 2. Rewrite the equation (a) log4(y) = x in exponential form (b) 10^(x2) = w in logarithmic form 3. Simplify (a) e^(In(5)) (b) In(e-*) (c) In^(log(b)) (d) log(107) 4. Suppose you know that logo(5) = 1.161 and log.(6) = 1.292. Evaluate (a) log.(30) (b) logb(25) (c) logb(1.2) 5. On the same graph, graph y = 10* and y =log(x). 6. Let f(x) = e^(-x2). What is the maximum value of this function? Is this function even, odd, or neither? 7. Combine log.(x) - 2log.(4) into one logarithm. 8. Solve for x (a) In(x2) = In(2x + 3) (b) 2.109x = 29 9. What is the value of an account after six years if you start with $10,000 and the interest rate is 6% compounded annually? Compounded monthly? 10. The population of a fast-growing town is expected to increase by 7% each year for the next three years. If the town has 5000 people today, how many is it predicted to have in three years? 11. At the end of this year you receive $5000 which you place into an account earning 5% compounded annually. The same thing happens at the end of 2019, and you do the same thing, but in a separate account (with the same interest rate). For two more years, 2020 and 2021, the same thing happens. At the end of 2021, how much do you have in each account? How much in total? Show that the formula for future value given in the introduction to this exam produces the same value