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MasterMindXD

  • 2 years ago

How to solve 10^[(10^(x+11)) +(0.5^(x+11))] =0

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  1. Ishaan94
    • 2 years ago
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    not possible i don't think a^(n) = 0 is possible

  2. MasterMindXD
    • 2 years ago
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    Well, this is what I had before....log(log(x+11))=log^((1/2)^(x+11)).

  3. Ishaan94
    • 2 years ago
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    oh okay

  4. Ishaan94
    • 2 years ago
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    log^((1/2)^(x+11))??

  5. MasterMindXD
    • 2 years ago
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    yeah

  6. Ishaan94
    • 2 years ago
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    i am assuming it's \[\log_{10} \log_{10} (x+11) = \log_{10} \frac{1}{2^{x+ 11}}\]

  7. MasterMindXD
    • 2 years ago
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    okay yeah...

  8. cristiann
    • 2 years ago
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    The equation log(x+11)=((1/2))^{x+11} has a unique solution, which cannot be found exactly (or guessed ... :) ) The existence is proved by Darboux-type reasoning: for x=-10: log1=0<(1/2)^1=1/2 for x=-1: log10=1>(1/2)^10 Unicity is proven by monotonicity ... :)

  9. cristiann
    • 2 years ago
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    The unique solution may be found numerically to be x=-9.5559 Darboux-type reasoning refers to: f(x1)<0 and f(x2)>0 and f() continuous then there is at least one value x0 between x1 and x2 such that f(x0)=0

  10. cristiann
    • 2 years ago
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    :)

  11. Ishaan94
    • 2 years ago
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    wow cristiann, you're awesome at mathematics

  12. cristiann
    • 2 years ago
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    Thanks ... not really ... just older ... :)

  13. cristiann
    • 2 years ago
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    And I'm taking you all the fun of doing them ...:)

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