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anonymous

  • 5 years ago

evaluate the following: log9 27

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  1. anonymous
    • 5 years ago
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    do you know how to convert bases?

  2. anonymous
    • 5 years ago
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    no ;(

  3. anonymous
    • 5 years ago
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    okay logarithms work the following way: any number can be expressed as another number to some power For example 13 can be expressed as 10 to the power 1.114

  4. anonymous
    • 5 years ago
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    here, 10 is called the base.

  5. anonymous
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    so log10 13 = 1.114 This means that logarithm of 13 to the base 10 is 1.114

  6. anonymous
    • 5 years ago
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    but im doing log 9?

  7. anonymous
    • 5 years ago
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    13 can also be expressed as 2 to the power 3.7004. which means log 2 13 = 3.7004

  8. anonymous
    • 5 years ago
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    would log9 be converted to 3?

  9. anonymous
    • 5 years ago
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    so log9 27 = ? the ? is the power to which you have to raise 9 in order to get 27. http://www.sosmath.com/algebra/logs/log4/log43/log43.html

  10. anonymous
    • 5 years ago
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    3?

  11. anonymous
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    following the logic of that link, we can say that log9 27 = log3 27/ log3 9

  12. anonymous
    • 5 years ago
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    now, what is log3 27?

  13. anonymous
    • 5 years ago
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    so i was rite?

  14. anonymous
    • 5 years ago
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    no.

  15. anonymous
    • 5 years ago
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    ugh.

  16. anonymous
    • 5 years ago
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    answer my question. what is log3 27?

  17. anonymous
    • 5 years ago
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    explain it in plain english for now.

  18. anonymous
    • 5 years ago
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    9?

  19. anonymous
    • 5 years ago
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    no, read what I posted earlier. Don't simply dab at answers. Understand the logic behind logs and you wont ever have any more problems with it.

  20. anonymous
    • 5 years ago
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    its harrd. okay, we would put log3/log3 27?

  21. anonymous
    • 5 years ago
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    do you understand the meaning of logs? I posted it earlier. READ through it.

  22. anonymous
    • 5 years ago
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    it is not hard at all.

  23. anonymous
    • 5 years ago
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    what is 4 to the power 2?

  24. anonymous
    • 5 years ago
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    ya its hard im not a smart cookie like you. i dont no where you got the decimals from your example???!!

  25. anonymous
    • 5 years ago
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    2?

  26. anonymous
    • 5 years ago
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    okay. I am trying to explain it to you. what is 4 squared? what we mean by 4 raised to the power 2 is 4 squared.

  27. anonymous
    • 5 years ago
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    oh yah okay thats simple

  28. anonymous
    • 5 years ago
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    so give me the answer. what is 4 raised to the power 2?

  29. anonymous
    • 5 years ago
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    4^2

  30. anonymous
    • 5 years ago
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    right, what is the value of 4^2? 4^2 = 4*4 right? what is 4*4?

  31. anonymous
    • 5 years ago
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    16

  32. anonymous
    • 5 years ago
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    just give me the number. Use your calculator.

  33. anonymous
    • 5 years ago
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    right. okay great!. what is 4 raised to the power 3?

  34. anonymous
    • 5 years ago
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    4^3

  35. anonymous
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    i know my powers mister

  36. anonymous
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    thats good to know. I am asking the value of 4^3.

  37. anonymous
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    48

  38. anonymous
    • 5 years ago
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    it is 64.

  39. anonymous
    • 5 years ago
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    i multiplyed it wrong. sorry

  40. anonymous
    • 5 years ago
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    anyway, the point is this. what if you wanted to express a number between 16 and 64 as a power of 4? what happens then?

  41. anonymous
    • 5 years ago
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    find the number in the middle?

  42. anonymous
    • 5 years ago
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    I want you to express the number 32 as a power of 4. Can you do it?

  43. anonymous
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    what if I wanted 17 as a power of 4, or 18?

  44. anonymous
    • 5 years ago
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    ya 4 times 8

  45. anonymous
    • 5 years ago
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    no

  46. anonymous
    • 5 years ago
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    what is the value of log base 5 512

  47. anonymous
    • 5 years ago
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    no no. that is 4 times 8, I want you to express 32 as a power of 4. You can express 16 as the 2nd power of 4 and 64 as the 3rd power of 4. what about 17, 18 , 19 and so on?

  48. anonymous
    • 5 years ago
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    without calculator

  49. anonymous
    • 5 years ago
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    you cant? it would be in a decimal rite?

  50. anonymous
    • 5 years ago
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    exactly! you are on the right track margaret! very well done!

  51. anonymous
    • 5 years ago
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    thankyou!

  52. anonymous
    • 5 years ago
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    conditions are given like log 2 = 0.3010 and log 3= 0.4771......so whats the value of log base 5 512?

  53. anonymous
    • 5 years ago
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    okay. so that is where we use logarithms. so 4 should be raised to a power between 2 and 3 in order to get 32 right?

  54. anonymous
    • 5 years ago
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    idk sathiprakash

  55. anonymous
    • 5 years ago
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    sathiprakash if you have a separate problem please post it elsewhere. you are confusing the learning process here.

  56. anonymous
    • 5 years ago
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    ok.

  57. anonymous
    • 5 years ago
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    right

  58. anonymous
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    okay margaret, now, so we know that 4^2 is 16 and 4^3 is 64. so to express 32 as a power of 4, we know that the answer must lie between 2 and 3. correct?

  59. anonymous
    • 5 years ago
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    do you have a calculator, margaret?

  60. anonymous
    • 5 years ago
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    right so it would turn into a decimal

  61. anonymous
    • 5 years ago
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    i can get it

  62. anonymous
    • 5 years ago
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    okay doesnt matter. use google. it has a calculator built in. paste this exactly. 4^2.5

  63. anonymous
    • 5 years ago
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    just copy paste that in google.

  64. anonymous
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    =32

  65. anonymous
    • 5 years ago
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    great! so you see? any number can be expressed as a power of 4!

  66. anonymous
    • 5 years ago
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    even my problem log9 27

  67. anonymous
    • 5 years ago
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    So we call 4 the base. similarly in your problem, the base is 9.

  68. anonymous
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    so we need to find what power we need to raise 9 to get 27.

  69. anonymous
    • 5 years ago
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    so it will convert to 3

  70. anonymous
    • 5 years ago
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    right, so what we do is, we convert bases, that is a logarithmic property. I pasted that link earlier. so log9 27 = log3 27/log3 9

  71. anonymous
    • 5 years ago
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    so what power do you need to raise 3 to get 27? do you know?

  72. anonymous
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    what is 3^3?

  73. anonymous
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    9?

  74. anonymous
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    no, try again.

  75. anonymous
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    wait no its 3

  76. anonymous
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    no. 3^3 = 3*3*3 correct?

  77. anonymous
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    yes

  78. anonymous
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    so what is 3 times 3 times 3?

  79. anonymous
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    27

  80. anonymous
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    great! so what is log3 27? In other words, what power do you need to raise 3 in order to get 27?

  81. anonymous
    • 5 years ago
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    3

  82. anonymous
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    very good! so then by the same logic, what is log3 9?

  83. anonymous
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    27

  84. anonymous
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    no, understand what log3 9 means. It means what power do you need to raise 3 to get 9. that is what log3 9 means.

  85. anonymous
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    so, try again. what does log3 9?

  86. anonymous
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    2?

  87. anonymous
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    very good!

  88. anonymous
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    so what is log3 27 / log3 9?

  89. anonymous
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    3/2

  90. anonymous
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    good. so your answer is 1.5. now go ahead and check your answer. see if 9^1.5 is 27

  91. anonymous
    • 5 years ago
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    go on, type it in google.

  92. anonymous
    • 5 years ago
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    it is

  93. anonymous
    • 5 years ago
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    thankyou very much

  94. anonymous
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    so log9 27 = 1.5 in english, it means that logarithm to the base 9 of 27 is 1.5 in other words. raise 9 to the power 1.5 to get 27.

  95. anonymous
    • 5 years ago
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    you are welcome. I hope you understood the meaning behind logs and powers and bases.

  96. anonymous
    • 5 years ago
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    yes sir i do now

  97. anonymous
    • 5 years ago
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    good, I want you to do a little exercise. just pick a number. say 7. let 7 be your base. raise 7 to 1.2, 1.3,1.4, 2.54444 etc and see what numbers you get in google. You will see that any number can be expressed as a power of 7. not just integers, even fractions can be expressed as powers of 7.

  98. anonymous
    • 5 years ago
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    alright i will

  99. anonymous
    • 5 years ago
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    okay. good. bye now.

  100. anonymous
    • 5 years ago
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    go ahead, take a medal then.

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