1. log(.01) = -2 because 10^-2 = 1/10^2 or .o1 similarly, log(10) = 1 and log(1) = 0. Plot (.01,-2) (0,1) and (1,10) the next point to the right would be (2,100) and (3,1000) Connect these points. Note x must always be greater than 0, since log(x) = 0 means what power car you raise 10 to in order to get 0. You cannot do this. as x gets closer to 0, it gets more and more negative.
2. 101000 1 in the 32 column and 1 in the 8 column is 40.
3. What power do you need to raise 3 to in order to get 30. 3^2 is 9..too small. 3^3 = 27.. too small. 3^4 = 81.. too big. So, log (base 3) of 30 is between 3 and 4. much closer to 3. so 3.1 would be a good guess
4. 5^3.3 = 202
5. log(3.16) = .5 (note.. log with no other notation means log(base 10)
6. log(2) + log(2) + log(x) + log(x)
7. log(6/x)
8. 10^t = 50. log(10^t) = log(50) which equals tlog(10)=log(50) by the log power rule. divide both sides by log(10) to get: t = log(50)/log(10) You can leave your answer in this form, but log(10) = 1 to that would be just t = log(50)
9. 5000(1.o4)^t = 50000. Divide both sides by 5000 so you can get the exponent term by itself. This gets you 1.04^t = 10. Now take the log of both sides to get: log(1.04^t) = log(10). By the log power rule, this equals t log(1.04) = log(10) Divide both sides by log(1.04) to get t = log(10)/log(1.04) leave as this or find t with a calculator
10. a and y are the corresponding sides. a = 5 and y = 2. Their ration is 5/2 or 2.5. Therefore, you have to multiply the smaller side by 2.5 to get the larger corresponding side, or divide by 2.5 to get the smaller side. b = 6(2.5) or 15. z = 15/2.5 or 6
11. The opposite side of angle b is side B, The adjacent side of angle b is side C
12. sin b = 5/13
13. tan b = 5/12
14. cos b = 12/13
15. Find the angle that gives the sin of 5/13 or .3846. Use arcsin function or try angles to find arcsin (.3846) = a little over 22 degrees.. ie sin(22) = about .3846
16. the 50 foot pole will be the hypotenuse. You want to find the height of the tree, which is the side opposite of the 65 degree angle. Therefore, sin(65) = x/50, where x is the height of the tree. Using your calculator, this equals .9063 = x/50. multiply both sides by 50 to get: 45.31 = x