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    :confused:

    find the value of m when: sqaure root 128 = 2 to the power of m

    How in the world do I do this? What are the basic steps please someone tell me
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    (Original post by jasons61)
    :confused:

    find the value of m when: sqaure root 128 = 2 to the power of m

    How in the world do I do this? What are the basic steps please someone tell me
    2^m = 128^0.5

    128 can be expressed as a power of 2: 128 = 2^7

    2^m = (2^7)^0.5

    2^m = 2^3.5 (multiply powers)

    Bases are the same, therefore powers are the same => m = 3.5
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    (Original post by jasons61)
    :confused:

    find the value of m when: sqaure root 128 = 2 to the power of m

    How in the world do I do this? What are the basic steps please someone tell me
    Ignore the square root to start with, and concentrate on the 128. Starting with 2, what power of 2 is 128? Well 128 = 2x2x2x2x2x2x2 = 2^7. The square root of a number x = x^(1/2). Can you finish from there?
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    this is nice and easy


    (128)^0.5 = 2^m

    128 = 2^2m

    now there are two methods one is basic other is avanced:

    method 1 (advanced)

    log both sides to get:

    log(128) = 2m (log2)

    log(128)/log(2) = 2m

    7 = 2m

    m = 7

    method 2 (easy)

    (128) = 2^2m

    you shoudl realise that 128 also equals 2 to the power of 7

    so 2^7 = 2#^2m

    therefore: 7 = 2m

    and m = 7, as before.

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    I don't know the step by step method... but you can work it out just by observation..

    2^m = (128)^0.5

    2^m = (2^X)^0.5


    where (2^X) = 128
    >That calculation is easy...

    as 128
    64 (2^6)
    32 (2^5
    16 (2^4
    8 (2^3
    4 (2^2
    2 (2^1

    ie 2^7

    Therefore 2^m = (2^7)^0.5

    Times The Powers

    Therefore, 2^m = 2^ 3.5

    Therefore m = 3.5
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    i got a better one
    ROOT 128 = 2^m
    128 = 2^2m
    log 128 = 2m log 2
    log 128 / log 2 = 2m
    7 = 2m
    m = 3.5

    cut the boring factorisation
    just use your calculators
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    Looks like he's doing GCSE, so won't need logs..
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    I found a better method, a P1 method. Im gonna use ¬ as squared root.

    What you do is simplify the ¬128.
    = ¬128 = ¬64 x 2 = 8¬2

    Therefore 8¬2 = 2^m

    From P1, you should know that a¬b = b^1/a

    Therefore using this method m = 1/8

    Someone confirm this please.
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    Your use of a¬b = b^(1/a) isn't right....
    e.g.
    b^(1/3) is the cube root of b, not 3x¬b
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    (Original post by another_katie)
    Your use of a¬b = b^(1/a) isn't right....
    e.g.
    b^(1/3) is the cube root of b, not 3x¬b

    I never said there was an x involved.
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    sorry, i meant 3 times ¬b
    (3 lots of root b) isn't equal to b^(1/3) because that's the cube root of b, not three times the square root of it....
 
 
 
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