PLEASE SHOW ALL WORK!

1) write 4^3 = 64 in log form.

2) write n^3x = m in log form.

3) write log9 27 = 3/2 in exponential form.

4) solve for y: log2 16 = 3y.

5) solve for x: log5 (2x-5) = 3

6) Using the properties of logs, log (3a^2 / b) could be written as: (expand as far as possible)

7) Restate as a SINGLE log: 3ln x - 4ln y.

8) Restate as a SINGLE log: 5log2 x - log2 y + 4log2 z.

9) Find: log7.2 91.

10) Find: ln1/5

11) Solve for x: ln e^8x = 4.

12)Solve for y: log1/5 25 = y.

13) Sole for x: 9^x = 103.

14) sove for x: 4^x+1 = 7^x.

15) Solve for x: log ( x+20) = 2log x.

16) Solve for x: log (5x + 40) - 2 = log x.

17) The population of a city grows according to P = Ae^nt where projected population is P, starting population is A, time in years is t, and n is an observed or expected rate of increase in population ( in decimal form). If a city of 120,00 has an expected growth rate of 7%, how big will it be in 5 years?

18) A population of a city grows according to P = Ae^nt. If it took 14 years for a certain city to increase in size from 135,000 to 210,000, what was its rate of growth n? (HINT: remember n will be in decimal form when found. ANSWER should be in percent form)

19) For interest compounded continuously, the total amount P is given by P = Ae^rt where A is the initial amount invested, r is the yearly rate and t is the time in years. Find to the nearest tenth of a year how long it will take to DOUBLE an investment when it is invested at 4.5% compounded continuously.

PLEASE SHOW ALL WORK!