Hw31+application+of+logs

15. 3^x = 30 Log 3^x = Log 30 - Take the log of both sides X Log3 = Log 30 - Move the x to the front of the log X= Log 30/Log 3 – Divide log 3 on both sides = 3.10

17. 5.6^x = 56 Log 5.6^x = Log 56 – Take the log of both sides X Log 5.6 = Log 56 - Move X to front of Log X= Log 56/ Log 5.6 - Divide by 5.6 on both sides = 2.34

19. 30^-x = Log 5 -x Log 30 = Log 5 - Take log of both sides -X = Log 5/Log 30 - Dive by log 30 on both sides, x remains negative = -.473

21. 3.5^2x = 60 Log 3.5 ^2x = Log 60 - Take log of both sides 2x Log 3.5 = Log 60 - move 2x to front of equation 2x = Log 60/ Log 3.5 - Divide by log 3.5 on both sides = 1.63

23. 4x= 8 root 2 2^2x = 2^7 – Make bases common, common base is 2 2x = 7 – set exponents are equal to each other x=7/4

25. 125x = 25 root 5 5^3x = 5^3 - Make bases common, common base is 5 = 5/6 - Set bases equal and solve

27. x^2/5 = 34 x^2 to the fifth root = 34 Log x^2/5 = Log 34 - Take the log of both sides 2/5 Log x = Log 34 - Move 2/5 to the front of the log 2/5 = Log 34/Log x - Divide by log x on both sides 2/5 = Log 34/Log x = 6740 29. X^4 cubed= 60 – cube 60 and put the result to the fourth root X^4 squared = 21600 squared - take the fourth root of 21600 X= 21.6

31 . 2x^5 = 100 - divide by 2 on both sides x^5 = 50 - take the fifth root of 50 x= 50 root 5 - enter 50 to the fifth root into calculator x= 2.2

33. (3y -1)^6 = 80 – move 6 to front of equation 6 log (3y-1) 6Log 3y-1 = Log 80 - divide by 6 on both side Log 3y-1 = Log 80/6 - divide by log (assumed to be 10) 3y-1 = 10 Log 80/6 - subtract 1 3y = 10 log 80/6 – divide by 3 y = 10 (log 80/6)/3 – enter in calculator y = 1.03

35. Log2 9 - take log of both log 9/ log 2 - divide =3.17

37. Log3 40 - take log of both Log 40/Log 3 - divide 3.36

39. 3^2x-7*3^x+10=0 u=3x – set u equal to what it needs to be u^2 - 7u +10 = 0 - make new equation using u  (u-2) (u-5) – solve using quadratic or factoring u= 2,5 - make two separate equations 3^x = 2 3^x = 5 x = Log2/Log3 x= Log5/Log3 = .63 = 1.40