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    rearrange everything and make it in terms of 2:
    2^3x = (2^1/2)/(2^5)
    equate the indices : 3x = -4.5
    x=-1.5
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    (Original post by Bence9912)
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    Multiply both sides by root(8)
    Write everything as powers of 8
    Use rules of indices to simplify the powers.


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    (Original post by Sydian)
    rearrange everything and make it in terms of 2:
    2^3x = (2^1/2)/(2^5)
    equate the indices : 3x = -4.5
    x=-1.5
    How did you rearrange?
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    (Original post by Bence9912)
    How did you rearrange?
    multiply both sides by root 8, rationalise the right hand side, at this point i have
    8^x = root 2 / 32

    ie 2^3x = 2^1/2 / 2^5
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    (Original post by Bence9912)
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    times both sides by root 8 so 8^x = root 8 / 64. root 8/64 is the same as root 2/32 (surds and simplifying). which can be further simplified to 2^-9/2 due to the rule of indices(2^1/2 / 2^5). so 8^x = 2^-9/2. 8^x is the same as (2^x)^3 so therefore 2^x = cube root of 2^-9/2 = 2^-3/2. so 2^x = 2^-3/2. x = -3/2.
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    Get it in terms of powers of 8 is the easiest way, so you rearrange to get  8^x = (8^{-2}*8^{0.5}) = 8^{-1.5} and then comparing both sides shows x = -1.5

    You don't need to put it in powers of 2, or work with surds!
 
 
 
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