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    what will happen if I times log2X to log2X? Will it be (log2X)2? If it is, how do i solve this?
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    You're correct.
    You should get 2 values of x for this equation.
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    Notice 32=2^5 and 16=2^4. Use laws of logs... And then use part a
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    The values of  \log_2 32 \text{ and } \log_2 16 are just integers so the numerator simplifies very nicely.
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    log2 32 + log2 16 means you can multiply them. So its log2 515 / log2 x = log2 x

    multiply x to both sides

    log2 512 = (log2 x)^2

    if you type log2 512 into your calculator, that will be simplified down to 9

    sq root both sides

    +/- 3 = log2 x

    using log rules, this is saying x is equal to 2 to the power of plus or minus three.

    so x = 8 or 1/3

    sorry, its hard to explain logs without actually writing it out
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    (Original post by Mina_)
    log2 32 + log2 16 means you can multiply them. So its log2 515 / log2 x = log2 x

    multiply x to both sides

    log2 512 = (log2 x)^2

    if you type log2 512 into your calculator, that will be simplified down to 9

    sq root both sides

    +/- 3 = log2 x

    using log rules, this is saying x is equal to 2 to the power of plus or minus three.

    so x = 8 or 1/3

    sorry, its hard to explain logs without actually writing it out
    There's no need to multiply. If you notice 32=2^5 and 16=2^4 then you can evaluate the top without a calculator as 9. So 9/y=y, y^2=9 , y=±3 where y=log_2(x) as you said...

    Answers should be 8 and 1/8.
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    (Original post by alesha98)
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    what will happen if I times log2X to log2X? Will it be (log2X)2? If it is, how do i solve this?
    you can solve log_2 32\ and\ log_2 16\ and\ find\ out\ what\ they're\ equal\ to

    you can also sub log_2 x\ for\ U\ or\ another\ term if you find doing things with algebra help
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    (Original post by Math12345)
    There's no need to multiply. If you notice 32=2^5 and 16=2^4 then you can evaluate the top without a calculator as 9. So 9/y=y, y^2=9 , y=±3 where y=log_2(x) as you said...

    Answers should be 8 and 1/8.
    Sorry, I meant 1/8 !
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    (Original post by Mina_)
    Sorry, I meant 1/8 !
    Thanks, it is such an easy question but i overthinking it
 
 
 
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