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name: Mathematics 116 test three Thursday, November 18, 2004 please show your work to get full credit for each problem 1. Convert the equation ex = M to a logarithmic equation. 2. Convert the equation log H = p to an exponential equation. (3–4) Use a calculator to estimate the value of each expression to the nearest hundredth: 3. 800e(−.06)(30) 4. log2 17 5. The domain of y = log(x) is . (6–8) Simplify: 6. ln e2004 8. 10−2 log x 7. 10log x 9–10. If log M = .21 and log N = .35 then 9. log(M N ) = . M log N 10. = . page two 11. Solve for t: 800e−.06t = 50 13. Solve for x: 21−x = 3x 12. Solve for x: − log2 (−x) = 3 14. Rewrite without logarithms: log V = log C + 3 log r page three 15. Use the properties of logarithms to expand: 10x3 log √ 2x − 1 ! 16. A bank account offers interest at an annual percentage rate of 3.6%, compounded monthly. One sum of $ 1,000 is deposited into the account, and no further deposits or withdrawals are made. Only interest causes the account to grow. • How much money will the account contain after 20 years? • How many years will pass before the account contains $10,000 ?