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anonymous

  • 5 years ago

2( log 2 x − log y ) − ( log 3 + 2 log 5)

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  1. anonymous
    • 5 years ago
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    what are you supposed to do about it?

  2. anonymous
    • 5 years ago
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    solve it

  3. anonymous
    • 5 years ago
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    it is not an equation. you cant solve it.

  4. anonymous
    • 5 years ago
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    cant it be simplified?

  5. anonymous
    • 5 years ago
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    You want to simplify it?

  6. anonymous
    • 5 years ago
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    yes

  7. anonymous
    • 5 years ago
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    Is it log (2x), or log x to base 2?

  8. anonymous
    • 5 years ago
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    it is log((2x/y)^2)-log 75

  9. anonymous
    • 5 years ago
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    log 2x

  10. anonymous
    • 5 years ago
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    not that log a - log b = log(a/b) and log a +log b = log(ab)

  11. anonymous
    • 5 years ago
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    how did u get the answer dhatraditya?

  12. anonymous
    • 5 years ago
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    note*

  13. anonymous
    • 5 years ago
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    note also that xlog a = log a^x

  14. anonymous
    • 5 years ago
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    \[2 (\log(2x)-\log y)-(\log 3+2\log 5)=2(\log {2x \over y})-\log(3*5^2)\] =\[\log({2x \over y})^2-\log(75)=\log({4x^2 \over 75y^2})\]

  15. anonymous
    • 5 years ago
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    I think this is the simplest it can be.

  16. anonymous
    • 5 years ago
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    so its simplified form is log ((2x/y)^2/75))

  17. anonymous
    • 5 years ago
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    What AnwarA has.

  18. anonymous
    • 5 years ago
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    thank you so much

  19. anonymous
    • 5 years ago
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    You're welcome!

  20. anonymous
    • 5 years ago
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    how did u get the 75?

  21. anonymous
    • 5 years ago
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    3*5^2=3(25)=75

  22. anonymous
    • 5 years ago
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    as I explained, x log a = log a^x so 2 log 5 = log 5^2 = log 25 log a + log b = log (ab) now, log 3+ log 25 = log (3 times25) = log 75

  23. anonymous
    • 5 years ago
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    i understand now.thx

  24. anonymous
    • 5 years ago
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    you are welcome.

  25. anonymous
    • 5 years ago
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    solve log base x (5x+24)=2

  26. anonymous
    • 5 years ago
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    x = 8 or -3

  27. anonymous
    • 5 years ago
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    since logs are not defined for negative numbers, x = 8

  28. anonymous
    • 5 years ago
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    do you know how I arrived at the answer, leona?

  29. anonymous
    • 5 years ago
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    ?how did u work it out

  30. anonymous
    • 5 years ago
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    do you know how logarithms work?

  31. anonymous
    • 5 years ago
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    i know some of the rules

  32. anonymous
    • 5 years ago
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    tell me what you know about logs? what do you understand by logs?

  33. anonymous
    • 5 years ago
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    i know that the logarithm of 1 regardless of the base is one

  34. anonymous
    • 5 years ago
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    if i told you log 32 to the base 4 is 2.5, what do I mean by that?

  35. anonymous
    • 5 years ago
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    that 4 ^2.5 is 32

  36. anonymous
    • 5 years ago
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    exactly! good! have you tried that in your calculator?

  37. anonymous
    • 5 years ago
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    yes

  38. anonymous
    • 5 years ago
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    so you understand that any number can be represented as a power of another number?

  39. anonymous
    • 5 years ago
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    yes

  40. anonymous
    • 5 years ago
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    okay good. so what do i mean when i say log(5x+24) to the base x is 2?

  41. anonymous
    • 5 years ago
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    it means that x raise to the power 2 equal (5x+24)

  42. anonymous
    • 5 years ago
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    I should have said any POSITIVE number can be represented as apower of any other number (the base)

  43. anonymous
    • 5 years ago
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    right, so x^2 = 5x+24

  44. anonymous
    • 5 years ago
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    this is a simple quadratic equation

  45. anonymous
    • 5 years ago
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    should i square the x^2?

  46. anonymous
    • 5 years ago
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    why would you want to do that?

  47. anonymous
    • 5 years ago
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    i dont know how to remove the x

  48. anonymous
    • 5 years ago
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    okay have you solved quadratic equations before?

  49. anonymous
    • 5 years ago
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    yes

  50. anonymous
    • 5 years ago
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    can you see that x^2 = 5x+24 can be rearranged so that it is in the form ax^2+bx+c = 0?

  51. anonymous
    • 5 years ago
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    ohh yea

  52. anonymous
    • 5 years ago
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    after that it is straightforward factoring. Remember that you will get a negative root. You cannot use the negative root, because as I explained before, logarithms for negative bases are generally discarded.

  53. anonymous
    • 5 years ago
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    what r the two factors? cant find them

  54. anonymous
    • 5 years ago
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    post your equation.

  55. anonymous
    • 5 years ago
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    x^2-5x-24=0

  56. anonymous
    • 5 years ago
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    i got 8

  57. anonymous
    • 5 years ago
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    yeah!!!!!!

  58. anonymous
    • 5 years ago
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    did you use the quadratic formula or the factoring method?

  59. anonymous
    • 5 years ago
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    quadratic

  60. anonymous
    • 5 years ago
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    okay. anything that works, although in this case factoring is more elegant and efficient. remember, you have to discard the x= -3 root

  61. anonymous
    • 5 years ago
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    i did

  62. anonymous
    • 5 years ago
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    okay, do you know the reason why you discarded -3?

  63. anonymous
    • 5 years ago
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    because log not defined for negative numbers

  64. anonymous
    • 5 years ago
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    no, its because logs with negative bases only work for even powers. anyway, good job! have a medal.

  65. anonymous
    • 5 years ago
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    ok thank you

  66. anonymous
    • 5 years ago
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    do a little homework assignment for me. Google "why logarithms are not defined for negative bases" and "why logarithms are not defined for negative numbers". it will help you understand logs much better. all the best!

  67. anonymous
    • 5 years ago
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    you are welcome.

  68. anonymous
    • 5 years ago
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    ill do that

  69. anonymous
    • 5 years ago
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    :)

  70. anonymous
    • 5 years ago
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    are u going to be online in the night?

  71. anonymous
    • 5 years ago
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    i dont know. I generally come here in my free time to help out.

  72. anonymous
    • 5 years ago
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    ohh cause i ave exam 2marow and i need more help with other topics

  73. anonymous
    • 5 years ago
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    oh.. you can post your questions here so that I get notifications and I'll try to answer them before tomorrow.

  74. anonymous
    • 5 years ago
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    ok am going to try this question log base x (5x+14)=2

  75. anonymous
    • 5 years ago
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    okay, lemme know how it works out. you should get 7

  76. anonymous
    • 5 years ago
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    logarithm are not defined for negative values because the log and In graphs have a vertical asymptotic line at x=0 which is the lower boundary of the graph ..in fact the limit as x approaches zero from the right hand side ,the function approaches infinity and that makes the zero point the maximum tolerable value for the x values less than zero

  77. anonymous
    • 5 years ago
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    i got 7....using the factoring method

  78. anonymous
    • 5 years ago
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    okay good.

  79. anonymous
    • 5 years ago
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    thank you

  80. anonymous
    • 5 years ago
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    your latest logarithm question will go like : \[5x +14=x^{2}\]

  81. anonymous
    • 5 years ago
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    so \[x ^{2}-5x-14=0 and then you solve with the quadratic formula \]

  82. anonymous
    • 5 years ago
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    need help with this 1....log base 4 (1) +log (25)

  83. anonymous
    • 5 years ago
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    so x= 7 or x=-2 but when you substitute the x=-2 the equation doesnt make sence so x=7 is the answer hope that was helpful

  84. anonymous
    • 5 years ago
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    okay, what does log base 4 (1) mean?

  85. anonymous
    • 5 years ago
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    log to base 4 to a number = 1

  86. anonymous
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    log base 4 of 1 means what power will you raise the number 4 to have a value of 1 so its like : 1=4\[^{x}\]

  87. anonymous
    • 5 years ago
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    it means that 4 raised to a number should be equal to 1. what is that number? we know that any number raised to the power 0 is 1. so log base 4 (1) is 0. so your equation simplifies to just log 25

  88. anonymous
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    like 4\[4^{x}=1 \]

  89. anonymous
    • 5 years ago
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    that means x=0

  90. anonymous
    • 5 years ago
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    because

  91. anonymous
    • 5 years ago
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    \[4^{0}\]

  92. anonymous
    • 5 years ago
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    ohh yeah thats a rule of logs

  93. anonymous
    • 5 years ago
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    yes. you should remember the basic rules of logs. Also, understand what logarithms mean. That way, even if you get stuck in your test, you can work it out.

  94. anonymous
    • 5 years ago
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    so 5^2=25

  95. anonymous
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    right, log 25 = log 5^2 = ?

  96. anonymous
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    yeah so the final answer is log 5^2=25

  97. anonymous
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    log 25 without a base specified means the base is a standard base of ten (10)

  98. anonymous
    • 5 years ago
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    so are you saying that 10^25 = 5^2, leona?

  99. anonymous
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    so it shd read like \[\log_{10} 25=x\]

  100. anonymous
    • 5 years ago
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    which means 25=\[10^{x}\]

  101. anonymous
    • 5 years ago
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    no am nt

  102. anonymous
    • 5 years ago
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    then what do yoou mean by log 5^2 = 25?

  103. anonymous
    • 5 years ago
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    sinse it doent ave a base its base 10 rite?

  104. anonymous
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    so x=\[x= \log 25/\log 10\]

  105. anonymous
    • 5 years ago
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    yes, we assume that the base is 10 if it is not specified

  106. anonymous
    • 5 years ago
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    yas since it doesnt have any base it means base ten ...youre rite

  107. anonymous
    • 5 years ago
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    so i should use the rule of change of base

  108. anonymous
    • 5 years ago
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    log 25 is simply log 5^2 = 2log5

  109. anonymous
    • 5 years ago
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    are you required to find the numerical value of log 25?

  110. anonymous
    • 5 years ago
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    if you are, just punch it in your calculator and you have your answer.

  111. anonymous
    • 5 years ago
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    no that was nt required

  112. anonymous
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    then it is simply log 25, which can be written as 2 log 5

  113. anonymous
    • 5 years ago
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    ok..

  114. anonymous
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    since we know that x log a = log a^x

  115. anonymous
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    ok i now understand that rule

  116. anonymous
    • 5 years ago
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    2logx-log(2+3x)=1

  117. anonymous
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    okay, use the identities. x log a = log a^x and log a - log b = log(a/b)

  118. anonymous
    • 5 years ago
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    ok

  119. anonymous
    • 5 years ago
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    take it one step at a time. what is 2 log x = ?

  120. anonymous
    • 5 years ago
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    log x^2

  121. anonymous
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    okay and what is log x^2-log(2+3x)?

  122. anonymous
    • 5 years ago
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    would it be base 10 since no base is given?

  123. anonymous
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    yes

  124. anonymous
    • 5 years ago
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    10^1

  125. anonymous
    • 5 years ago
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    is zero

  126. anonymous
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    no, i meant log a - log b is log(a/b) so log (x^2) = log (2+3x) = ?

  127. anonymous
    • 5 years ago
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    sorry log (x^2) - log (2+3x) = ?

  128. anonymous
    • 5 years ago
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    am stuck

  129. anonymous
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    okay it is log(x^2/(2+3x)

  130. anonymous
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    so log (x^2/(2+3x)) = 1

  131. anonymous
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    yes

  132. anonymous
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    so if log A to the base 10 is 1, what do i mean by that?

  133. anonymous
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    10^1=a

  134. anonymous
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    yes, so if i say log(x^2/(2+3x)) = 1, what do i mean by that?

  135. anonymous
    • 5 years ago
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    it means log 1 = x^2/2+3x

  136. anonymous
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    no, pay attention to the last two statements i made and post your answer. think about it carefully.

  137. anonymous
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    i still dont get it

  138. anonymous
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    if log a = 1 means a = 10^1 then log(x^2/(2+3x)) =1 means x^2/2+3x = 10^1

  139. anonymous
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    ohhhhhhhh...:)

  140. anonymous
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    now its just a quadratic equation. solve it and find the values of x

  141. anonymous
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    rearrange it for me plz

  142. anonymous
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    no, you can do this on your own. multiply both sides by 2+3x and post what you got.

  143. anonymous
    • 5 years ago
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    4+12x+9x^2=20 +30x

  144. anonymous
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    \[x ^{2}/(2+3x) = 10\]

  145. anonymous
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    multiply both sides by (2+3x) to get \[x ^{2} = 30x+20\]

  146. anonymous
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    yea i ave that down

  147. anonymous
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    I dont understand how you got 4+12x+9x^2=20 +30x

  148. anonymous
    • 5 years ago
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    do you know how to manipulate equations?

  149. anonymous
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    no

  150. anonymous
    • 5 years ago
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    i get it now

  151. anonymous
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    http://www.chem.tamu.edu/class/fyp/mathrev/mr-algeb.html

  152. anonymous
    • 5 years ago
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    ok

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