A Math questions that has bugged me for a while

• AmuletxHeart

  24 May 10, 02:20

  How to do question 7, 8c and 9b?

  Answers are very much appreciated.

• AmuletxHeart

  24 May 10, 02:30

• AmuletxHeart

  24 May 10, 02:38

  

• AmuletxHeart

  24 May 10, 02:44

  

• ChoCoChips

  24 May 10, 03:22

  hi.

  lets look at qn 7.

  first u need to find out the value of c.

  so what u do here is u put in values of x and y. (which in this case is 2 and 3, respectively.)

  therefore

  log2 4 = 2 log2 2 + c

  we know 2 log2 2 = log2 4.

  so c = 0.

  so what's left is

  log2 (y+1) = 2 log2 (x)

  therefore 

  y+1 = x^2

  y = x^2 - 1.

  dunno correct anot.

  heh

• ChoCoChips

  24 May 10, 03:35

  qn 9b.

  (log5 4)(log2 10)

  ----------------------

  (log25 10^0.5)

   

  here we have 2 logs of different bases.

  so we need to change them.

  in this case we change all of them to log25. 

   

  log5 4 is therefore log25 4/log25 5

  log2 10 is therefore log25 2/log25 10

   

  so we have

                            (log25 4/log25 5) X (log25 10/log25 2) 

                     ---------------------------------------------------------

                                                    (log25 10^0.5)

   

  log25 4 = 2 log25 2

  log25 5 = 0.5 --------------> cuz 5 is the sqrt of 25.

  log25 10^0.5 = 0.5 log25 10

   

  with these in mind, we can now simplify the equation.

  eventually we will arrive at

   

  (2/0.5) X (log25 10)

  ------------------------------

  0.5 log25 10

   

  which gives us 

   

  4 log25 10

  -----------------

  0.5 log25 10 

   

  = 8.

• ChoCoChips

  24 May 10, 03:41

  qn 8c.

   

  (xe^x)^2 = 30e^-x

   

  expanding the LHS,

  we get (x^2)(e^2x)

  now lets remove the e-x on the RHS

  so the equation now is

   

  (x^2)(e^3x) = 30

   

  ln(x^2)(e^3x) = ln 30

   

  then we can separate the LHS, as ln(ab) = ln a + ln b.

  ln (x^2) + ln (e^3x) = ln 30

  2 ln x + 3x = ln 30

  ln x = 3x/2 + (ln30)/2.

   

  hope i ish correct.

  heh

• wee_ws

  24 May 10, 07:59

  Hi AmuletxHeart,

    It will also be good to reflect on what learning gaps you have, after learning about the solutions. Thanks.

  Cheers,
  Wen Shih

• Hitman+

  24 May 10, 08:06

  chocochips.... u mean u still remeber natural log and normal log after so many decades?

• Hitman+

  24 May 10, 08:10

  remembers macross saga series only ..................throws fat white a maths book away!

• quailmaster

  24 May 10, 20:06

  check out this webpage for some notes on logarithms

  http://www.a-maths-tuition.com/2010/05/logarithms-part-iii.html

• AmuletxHeart

  26 May 10, 23:58

  I'm sorry for replying late, but today is the last day of school so I finally have time to revisit this forum. I will do a reflection on this topic ASAP, including areas which I'm always stuck at.