## anonymous 5 years ago 2( log 2 x − log y ) − ( log 3 + 2 log 5)

1. anonymous

what are you supposed to do about it?

2. anonymous

solve it

3. anonymous

it is not an equation. you cant solve it.

4. anonymous

cant it be simplified?

5. anonymous

You want to simplify it?

6. anonymous

yes

7. anonymous

Is it log (2x), or log x to base 2?

8. anonymous

it is log((2x/y)^2)-log 75

9. anonymous

log 2x

10. anonymous

not that log a - log b = log(a/b) and log a +log b = log(ab)

11. anonymous

how did u get the answer dhatraditya?

12. anonymous

note*

13. anonymous

note also that xlog a = log a^x

14. anonymous

$2 (\log(2x)-\log y)-(\log 3+2\log 5)=2(\log {2x \over y})-\log(3*5^2)$ =$\log({2x \over y})^2-\log(75)=\log({4x^2 \over 75y^2})$

15. anonymous

I think this is the simplest it can be.

16. anonymous

so its simplified form is log ((2x/y)^2/75))

17. anonymous

What AnwarA has.

18. anonymous

thank you so much

19. anonymous

You're welcome!

20. anonymous

how did u get the 75?

21. anonymous

3*5^2=3(25)=75

22. anonymous

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

i understand now.thx

24. anonymous

you are welcome.

25. anonymous

solve log base x (5x+24)=2

26. anonymous

x = 8 or -3

27. anonymous

since logs are not defined for negative numbers, x = 8

28. anonymous

do you know how I arrived at the answer, leona?

29. anonymous

?how did u work it out

30. anonymous

do you know how logarithms work?

31. anonymous

i know some of the rules

32. anonymous

tell me what you know about logs? what do you understand by logs?

33. anonymous

i know that the logarithm of 1 regardless of the base is one

34. anonymous

if i told you log 32 to the base 4 is 2.5, what do I mean by that?

35. anonymous

that 4 ^2.5 is 32

36. anonymous

exactly! good! have you tried that in your calculator?

37. anonymous

yes

38. anonymous

so you understand that any number can be represented as a power of another number?

39. anonymous

yes

40. anonymous

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

41. anonymous

it means that x raise to the power 2 equal (5x+24)

42. anonymous

I should have said any POSITIVE number can be represented as apower of any other number (the base)

43. anonymous

right, so x^2 = 5x+24

44. anonymous

this is a simple quadratic equation

45. anonymous

should i square the x^2?

46. anonymous

why would you want to do that?

47. anonymous

i dont know how to remove the x

48. anonymous

okay have you solved quadratic equations before?

49. anonymous

yes

50. anonymous

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

ohh yea

52. anonymous

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

what r the two factors? cant find them

54. anonymous

55. anonymous

x^2-5x-24=0

56. anonymous

i got 8

57. anonymous

yeah!!!!!!

58. anonymous

did you use the quadratic formula or the factoring method?

59. anonymous

60. anonymous

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

i did

62. anonymous

okay, do you know the reason why you discarded -3?

63. anonymous

because log not defined for negative numbers

64. anonymous

no, its because logs with negative bases only work for even powers. anyway, good job! have a medal.

65. anonymous

ok thank you

66. anonymous

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

you are welcome.

68. anonymous

ill do that

69. anonymous

:)

70. anonymous

are u going to be online in the night?

71. anonymous

i dont know. I generally come here in my free time to help out.

72. anonymous

ohh cause i ave exam 2marow and i need more help with other topics

73. anonymous

oh.. you can post your questions here so that I get notifications and I'll try to answer them before tomorrow.

74. anonymous

ok am going to try this question log base x (5x+14)=2

75. anonymous

okay, lemme know how it works out. you should get 7

76. anonymous

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

i got 7....using the factoring method

78. anonymous

okay good.

79. anonymous

thank you

80. anonymous

your latest logarithm question will go like : $5x +14=x^{2}$

81. anonymous

so $x ^{2}-5x-14=0 and then you solve with the quadratic formula$

82. anonymous

need help with this 1....log base 4 (1) +log (25)

83. anonymous

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

okay, what does log base 4 (1) mean?

85. anonymous

log to base 4 to a number = 1

86. anonymous

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

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

like 4$4^{x}=1$

89. anonymous

that means x=0

90. anonymous

because

91. anonymous

$4^{0}$

92. anonymous

ohh yeah thats a rule of logs

93. anonymous

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

so 5^2=25

95. anonymous

right, log 25 = log 5^2 = ?

96. anonymous

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

97. anonymous

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

98. anonymous

so are you saying that 10^25 = 5^2, leona?

99. anonymous

so it shd read like $\log_{10} 25=x$

100. anonymous

which means 25=$10^{x}$

101. anonymous

no am nt

102. anonymous

then what do yoou mean by log 5^2 = 25?

103. anonymous

sinse it doent ave a base its base 10 rite?

104. anonymous

so x=$x= \log 25/\log 10$

105. anonymous

yes, we assume that the base is 10 if it is not specified

106. anonymous

yas since it doesnt have any base it means base ten ...youre rite

107. anonymous

so i should use the rule of change of base

108. anonymous

log 25 is simply log 5^2 = 2log5

109. anonymous

are you required to find the numerical value of log 25?

110. anonymous

if you are, just punch it in your calculator and you have your answer.

111. anonymous

no that was nt required

112. anonymous

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

113. anonymous

ok..

114. anonymous

since we know that x log a = log a^x

115. anonymous

ok i now understand that rule

116. anonymous

2logx-log(2+3x)=1

117. anonymous

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

118. anonymous

ok

119. anonymous

take it one step at a time. what is 2 log x = ?

120. anonymous

log x^2

121. anonymous

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

122. anonymous

would it be base 10 since no base is given?

123. anonymous

yes

124. anonymous

10^1

125. anonymous

is zero

126. anonymous

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

127. anonymous

sorry log (x^2) - log (2+3x) = ?

128. anonymous

am stuck

129. anonymous

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

130. anonymous

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

131. anonymous

yes

132. anonymous

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

133. anonymous

10^1=a

134. anonymous

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

135. anonymous

it means log 1 = x^2/2+3x

136. anonymous

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

137. anonymous

i still dont get it

138. anonymous

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

139. anonymous

ohhhhhhhh...:)

140. anonymous

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

141. anonymous

rearrange it for me plz

142. anonymous

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

143. anonymous

4+12x+9x^2=20 +30x

144. anonymous

$x ^{2}/(2+3x) = 10$

145. anonymous

multiply both sides by (2+3x) to get $x ^{2} = 30x+20$

146. anonymous

yea i ave that down

147. anonymous

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

148. anonymous

do you know how to manipulate equations?

149. anonymous

no

150. anonymous

i get it now

151. anonymous
152. anonymous

ok