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anonymous

  • 5 years ago

solve for x: 2^x+1=8^x-2

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  1. anonymous
    • 5 years ago
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    Is that 2^(x+1)?

  2. anonymous
    • 5 years ago
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    yes

  3. anonymous
    • 5 years ago
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    Note you can write 8 as 2^3. Try using that

  4. anonymous
    • 5 years ago
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    so x=3/2?

  5. anonymous
    • 5 years ago
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    No. How did you come to that answer?

  6. anonymous
    • 5 years ago
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    reducing? im really not good at math

  7. anonymous
    • 5 years ago
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    So we can substitute 2^3 for 8 right. It becomes 2^(x+1)=[2^3]^(x-2). The right hand side can be simplified 2^(x+1)=2^3(x-2) Since the bases are the same, the exponents must be equal.

  8. anonymous
    • 5 years ago
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    x would = 2

  9. anonymous
    • 5 years ago
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    Did you equate the exponents: Like if i say a^x=a^y, x must be equal to y. So in our case x+1=3(x-2)

  10. anonymous
    • 5 years ago
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    x=7/2?

  11. anonymous
    • 5 years ago
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    Yes. Do you see how the substitution helped? It made the bases the same so we can conclude that the exponents are equal

  12. anonymous
    • 5 years ago
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    yes you smart cookie. thankyou!!

  13. anonymous
    • 5 years ago
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    :) Np

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