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Logarithms in one log

  1. Nov 16, 2016 #1
    1. The problem statement, all variables and given/known data
    can we put
    3log2(x)-4log(y)+log2(5)
    in one logarithm
    it try in all the ways but i can't find the solution .

    2. Relevant equations
    loga(b)=logx(b)/logx(a)
    log(b*a)=log(b)+log(a)

    3. The attempt at a solution
    log2(5x^3)-log(y^4)
    log2(5x^3)-log2(y^4)/log2(10)
     
  2. jcsd
  3. Nov 16, 2016 #2

    fresh_42

    Staff: Mentor

    There are also formulas for ##\log_2 a - \log_2 b## and ##\log_2 a^c## which you need here.
     
  4. Nov 16, 2016 #3
    i don't know that i should do
     
  5. Nov 16, 2016 #4

    fresh_42

    Staff: Mentor

    Well you have
    which I read as ##\log_2 5x^3 - \log_{10} y^4 = \log_2 5x^3 - \frac{1}{\log_2 10}\log_2 y^4##.
    Now you can use ##c \cdot \log_2 a = \log_2 a^c## and ##\log_2 a - \log_2 b = \log_2 \frac{a}{b}## to write all in a single ##\log_2## expression. (Of course with a constant ##c=\log_2 10##.)
     
  6. Nov 16, 2016 #5
    log2(5x^3/((log2y^4)^(1/log2(10))))
    then who i can write it as a single log i see three logs
     
  7. Nov 16, 2016 #6

    fresh_42

    Staff: Mentor

    You cannot get rid of the constant ##\log_2 10## if you are dealing with two different basis. Are you sure they are meant to be different?
    And you have one ##\log_2## too many in the application of the formulas.
     
  8. Nov 16, 2016 #7
    sory for that
     
  9. Nov 16, 2016 #8
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