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solve the simultaneous equations;
log x base 2-log y base 4=4,
log (x-2y)base 2=5

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  1. The second equation can be rewritten as log(x-2y) = 2^5

    The first equation is more complicated because you have different bases. You need to chane base 4 to base 2 by using the rule that allows for base changes.

    Once you do this, you can use the Law of Logs to combine the left side which will equal 2^4 or 16.

    Can you finish it now? Do you need more help?

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  2. I have a strong feeling that Jessica has a typo , and all the bases are base 2
    (assume when I write log (..) , I mean log2 (..) )

    from the 1st:
    log x - log y = 4 ----> x/y = 16 or x = 16y
    from the 2nd:
    log(x-2y) = 5 ---> x-2y =32

    use substitution:
    16 - 2y = 32
    14y = 32
    y = 16/7 , then x = 16(16/7) = 256/7

    (256/7 , 16/7) satisfies both "assumed" equations)

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