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mathmath333

  • one year ago

logarithm question

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  1. mathmath333
    • one year ago
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    solve \(\large \color{black}{\begin{align} \log_{10}(x^{3}+5)=3\log_{10}(x+2)\hspace{.33em}\\~\\ \end{align}}\)

  2. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & (a.)\ \dfrac{-2+\sqrt2}{2} \hspace{.33em}\\~\\ & (b.)\ \dfrac{-2-\sqrt2}{2} \hspace{.33em}\\~\\ & (c.)\ \text{both a.) and b.) } \hspace{.33em}\\~\\ & (d.)\ \text{none of these} \hspace{.33em}\\~\\ \end{align}}\)

  3. ParthKohli
    • one year ago
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    \[\log_{10}(x^3 + 5) = \log_{10}{(x+2)^3}\]\[\Rightarrow x^3 + 5 = x^3 + 6x^2 + 12x + 8\]\[\Rightarrow 6x^2 + 12x + 3 = 0 \]Choose the solution for which both logarithms are defined.

  4. mathmath333
    • one year ago
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    both a.) and b.)

  5. mathmath333
    • one year ago
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    ?

  6. ParthKohli
    • one year ago
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    Yeah, I guess so.

  7. mathmath333
    • one year ago
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    my book has given option d.)

  8. ParthKohli
    • one year ago
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    If you know that your answer is correct, why care about the book?

  9. mathmath333
    • one year ago
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    lol i am not sure

  10. mathmath333
    • one year ago
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    i dont have brains

  11. ParthKohli
    • one year ago
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    You're correct. Don't worry.

  12. mathmath333
    • one year ago
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    all options of book is correct except this ? suspictious

  13. ParthKohli
    • one year ago
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    Book bhi ek insaan ne hi likhi hai. As I said, your answer is correct.

  14. ganeshie8
    • one year ago
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    you may double check with wolfram

  15. ParthKohli
    • one year ago
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    So you're right.

  16. mathmath333
    • one year ago
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    ok thnx, by the way is there a condition like \(x^{3}+5>0\) and \((x+2)^{3}>0\)

  17. ParthKohli
    • one year ago
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    Yes, which is what I meant that the logarithms should be defined. Both roots satisfy both conditions.

  18. mathmath333
    • one year ago
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    how do i find value of \(5^{1/3}\) by pen paper to check

  19. ParthKohli
    • one year ago
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    You don't need to find the value of \(5^{1/3}\). Plug in \(1.4 \) for \(\sqrt 2\) and that should almost always work.

  20. mathmath333
    • one year ago
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    y i dont need that value

  21. ParthKohli
    • one year ago
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    You need to check if \(x^3 + 5 > 0\) and \(x+2>0\). The second one is easier than the first. The solutions you get are\[\frac{-2 + \sqrt 2}{2} \approx - 0.3 , \frac{-2 - \sqrt 2}{2} \approx -1.7 \]The second one is simple. The first condition, well, is satisfied the first root. The second root is a closer call but it satisfies the condition.

  22. ParthKohli
    • one year ago
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    satisfied for the first root*

  23. phi
    • one year ago
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    You are the victim of a typo.... it happens quite a bit in math books because it is very hard to check the answers....

  24. mathmath333
    • one year ago
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    no typo for x^3+5>0

  25. ParthKohli
    • one year ago
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    He's talking about the answer-key.

  26. mathmath333
    • one year ago
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    oh lol

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