## MTALHAHASSAN2 one year ago Solve> log (5x-2)=3

1. MTALHAHASSAN2

|dw:1433042081319:dw|

2. Nnesha

change log to exponential form |dw:1433042073554:dw|

3. Nnesha

$\huge\rm log=\log_{10}$

4. MTALHAHASSAN2

|dw:1433042120636:dw|

5. Nnesha

|dw:1433042242477:dw| 3 should be exponent of base and base is 10

6. MTALHAHASSAN2

so it be 10 ^3

7. Nnesha

yep right

8. MTALHAHASSAN2

ok

9. MTALHAHASSAN2

10^3 be 1000 right

10. Nnesha

yep

11. MTALHAHASSAN2

so everyone time log base be 10

12. Nnesha

yep log = log_{10}

13. MTALHAHASSAN2

oh ok

14. MTALHAHASSAN2

|dw:1433042706292:dw|

15. MTALHAHASSAN2

is it be the same thing

16. MTALHAHASSAN2

so base be 10 for this one too

17. Nnesha

what is .04? is it exponent ?

18. MTALHAHASSAN2

|dw:1433042799032:dw|

19. Nnesha

$\huge\rm log 10^{-2} = .04$ like this ?

20. MTALHAHASSAN2

I do it like that but did not get the same answer

21. MTALHAHASSAN2

|dw:1433042894115:dw|

22. Nnesha

nope i'm asking which one is the original question ?

23. MTALHAHASSAN2

|dw:1433042957068:dw|

24. MTALHAHASSAN2

this one

25. Nnesha

$\log x^{.04} = -2$ like this ?

26. Nnesha

.04 is exponent ?

27. MTALHAHASSAN2

no it is 0.04

28. MTALHAHASSAN2

yes it is

29. Nnesha

yep 0.04 is same as .04

30. MTALHAHASSAN2

x^0.04

31. MTALHAHASSAN2

so I am doing it right

32. Nnesha

|dw:1433043171981:dw| you should move whole thing to the right side x^0.04

33. Nnesha

then apply power property

34. Nnesha

and $\huge\rm 10^{-2} = ???$

35. MTALHAHASSAN2

1/100

36. MTALHAHASSAN2

right

37. Nnesha

yep right

38. MTALHAHASSAN2

what you get

39. MTALHAHASSAN2

I am getting like -0.03

40. Nnesha

mhmm take a screenshot of the question

41. MTALHAHASSAN2

how

42. Nnesha

with lightshot or hit prntScr in the keyboard

43. MTALHAHASSAN2

|dw:1433043746800:dw|

44. MTALHAHASSAN2

|dw:1433043795538:dw|

45. Nnesha

how did you subtract -,04 it is an exponent you can't do that

46. MTALHAHASSAN2

47. MTALHAHASSAN2

@Nnesha

48. MTALHAHASSAN2

plz help me

49. Australopithecus

DO you still need help with this?

50. Nnesha

i'm soooo sorry *internet issues* sorry!!! :(

51. MTALHAHASSAN2

@Nnesha

52. MTALHAHASSAN2

know can you plz help me with that question

53. Nnesha

ohh u back let's do it !

54. MTALHAHASSAN2

ok sure

55. MTALHAHASSAN2

|dw:1433093342529:dw|

56. MTALHAHASSAN2

so we left from their

57. Nnesha

$\huge\rm 10^{-2} = x^{0.04}$ 10^{-2} = 1/100 $\large\rm \frac{ 1 }{ 100}=x^{0.04}$

58. Nnesha

do you have a answer choices ?

59. MTALHAHASSAN2

no

60. MTALHAHASSAN2

what can we do after this step

61. Nnesha

okay not take ln both side and apply power rule

62. Nnesha

now*

63. Nnesha

$\huge\rm 10^{-2} = x^{0.04}$ 10^{-2} = 1/100 $\large\rm \frac{ 1 }{ 100}=x^{0.04}$ 1/100 = .01 $\large\rm 0.01=x^{0.04}$ we take ln both sides $\large\rm \color{reD}{ln} 0.01= \color {red}{ln}x^{0.04}$

64. Nnesha

power prop.$\large\rm ln x^y = y \ln x$ apply it

65. MTALHAHASSAN2

what you mean the In

66. MTALHAHASSAN2

by*

67. Nnesha

natural log have u learned it ?

68. Nnesha

natural log and *e" ??

69. Nnesha

do you know about it ?

70. MTALHAHASSAN2

I think I do

71. Nnesha

alright good :-)

72. Nnesha

$\large\rm \color{reD}{ln} 0.01= \color {red}{ln}x^{0.04}$ try it :-)

73. Nnesha

ello?

74. MTALHAHASSAN2

ok

75. MTALHAHASSAN2

|dw:1433095640902:dw|

76. MTALHAHASSAN2

is it be like that

77. Nnesha

you have to take ln both sides so that suppose to be $\huge\rm ln 0.01 = .04 \ln x$ now divide both side by 0.04

78. MTALHAHASSAN2

but why we are dividing both side with 0.04

79. Nnesha

we have to solve for x so we have to divide both sides by .04 when u will left with ln x at the right side side after that you can take *e* both side to cancel out ln

80. Nnesha

$\huge\rm ln 0.01 = .04 \ln x$ here you can't take *e* bec there is .04 at front of ln

81. MTALHAHASSAN2

|dw:1433096812958:dw|

82. MTALHAHASSAN2

is 0.25 be x

83. Nnesha

wait let me check

84. Nnesha

nope it's ln (.01) divide by .04 not just .01/.04

85. Nnesha

x is the base right ?? now tell me which one is your question $\huge\rm log x^{0.04} = -2$ or $\huge\rm log_x 0.04 =-2$ which one is it ?

86. MTALHAHASSAN2

second one

87. MTALHAHASSAN2

logx0.04=−2

88. triciaal

The log of a number is the power to which the base must be raised to get that number.

89. triciaal

as shown by @Nnesha |dw:1433111045071:dw|

90. triciaal

|dw:1433111216199:dw|

91. triciaal

|dw:1433111397216:dw|

92. triciaal

|dw:1433111901139:dw|

93. triciaal

|dw:1433112029139:dw|

94. dmndlife24

Something you should probably memorize: The logarithm is the exponent you put on the base to get the argument.

95. Nnesha

ahh alright i asked yesterday http://prntscr.com/7bnzx0 and u said yes .04 is a exponent

96. Nnesha

so if it's a 2nd one then x is base of log

97. Nnesha

after converting it to exponential form it should be $\huge\rm x^{-2} = .04$ apply exponent rule x^{-m} = 1/m and then cross multiply

98. MTALHAHASSAN2

I knwo

99. Nnesha

so u got the answer ?let me know what u get :-)

100. MTALHAHASSAN2

I get 0.25/ or 0.004

101. Nnesha

how did you get .25 ?

102. Nnesha

$\log_x 0.04 = -2$ ^^^tha$x^{-2} = ???$t is your question change to exponential form $\huge\rm x^{-2} = 0.04$ now $x^{-2}= ???$

103. MTALHAHASSAN2

0.01/0.04

104. MTALHAHASSAN2

but isn't log base be 10

105. Nnesha

nope that's not right we did it wrong bec i thought it's $\log x^{0.04}= -2$ but that's wrong your question is $\log_x 0.04 = -2$ x is base of log

106. Nnesha

log = log_10 but in that question given base is x

107. Nnesha

when they just gave you log without any base then you need to use 10

108. MTALHAHASSAN2

oh ok

109. Nnesha

|dw:1433112209702:dw|' now solve this

110. MTALHAHASSAN2

|dw:1433112345039:dw|

111. MTALHAHASSAN2

right

112. Nnesha

yep right cross multiply then solve for x

113. MTALHAHASSAN2

|dw:1433112422389:dw|

114. Nnesha

yep right solve for x^2

115. MTALHAHASSAN2

|dw:1433112507437:dw|

116. Nnesha

-.04 ?

117. Nnesha

0.04 is multiplying with x^2 how would you cancel it ?

118. MTALHAHASSAN2

|dw:1433112651173:dw|

119. Nnesha

nope nope

120. MTALHAHASSAN2

oh

121. Nnesha

1 = 0.04x^2 what is opposite of multiply ? do that to cancel out .04 from right side

122. MTALHAHASSAN2

|dw:1433112883319:dw|

123. Nnesha

perfect!

124. MTALHAHASSAN2

thnx a lot again

125. Nnesha

my pleasure :-) great work!