Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Logarithm?

a) Express log4(x) in terms of log2(x)

b)Express log8(y) in terms of log2(y)

c) Hence solve the simultaneous equations

          6log4(x) =3log8(y)=16

           log2(x) -2log4(y) =4

3 Answers

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  • Vaman
    Lv 7
    4 weeks ago

    a) Express log4(x) in terms of log2(x)

    b)Express log8(y) in terms of log2(y)

    c) Hence solve the simultaneous equations

              6log4(x) =3log8(y)=16

               log2(x) -2log4(y) =4

    a) Express log4(x) in terms of log2(x), let log 4(x)=y. x= 4^y = 2^(2y) ,

    Take log wrt 2. log 4(x)=y,  log 2 x= 2y, log 4(x)= 2 log 2 (x)

    Similarly, b will have log 8 (y) = 3 log 2 (y).

    c) Follow this and write

    6 log 4x =12 log 4(y)=16,  3 log 4(x) -6 log4(y)=8.

    In terms of base 2, it will be  6 log 2(x) -12 log 2(y)=8

    The second equation  is log 2x -4 log 2y=4. put log 2(x)= a, and log 2(y)=b

    3a-6b=8. a-4b=4, multiply the second equation by 3 and subtract.

    12b-6b=4=6b, b=2/3.

    a=4*2/3+4=20/3=log2(x), x= 2^(20/3), y= 2^(2/3)

  • 4 weeks ago

     Solving logarithmic equation are explained here in details so that student can ... Therefore, x = 6. (ii) 0.000001 to the base 0.01. Solution: Let y be the required logarithm. ... If 3 + log10 x = 2 log10 y, find x in terms of y.

  • Bryce
    Lv 7
    4 weeks ago

    a. 2log2 x= log4 x

    b. 3log2 y= log8 y

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