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Math Help - help plz

  1. #1
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    help plz

    4^x+2 = 32^x

    you would have to change the base of 4, right? so would it become 32^8x+16? and then cancel the bases and set 8x + 16 = x?

    then what's the next step?

    hm.
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by borkthis View Post
    4^x+2 = 32^x

    you would have to change the base of 4, right? so would it become 32^8x+16? and then cancel the bases and set 8x + 16 = x?

    then what's the next step?

    hm.
    Do you mean

    4^x + 2 = 32^x

    4^{x+2} = 32^x

    Remember that 4, 2 and 32 are all powers of 2
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  3. #3
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    the second form is what i meant. 4 to the power of x + 2. i'm having trouble figuring out the correct way of changing base and solving for x.
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  4. #4
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    Quote Originally Posted by borkthis View Post
    the second form is what i meant. 4 to the power of x + 2. i'm having trouble figuring out the correct way of changing base and solving for x.
    4^{x+2} = 32^x

    As these are both powers of 2 change to base 2:

    (2^2)^{x+2} = (2^5)^x

    because (a^b)^c = a^{bc}

    2^{2x+4} = 2^{5x}

    Now they have the same base so equate the exponents and solve
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  5. #5
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    YES! thank you so much! i was doing something completely off.
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