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vivalakoda

  • 2 years ago

I need help with an IMPOSSIBLE equation?

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  1. Troublemaker
    • 2 years ago
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    Well what is it?...

  2. vivalakoda
    • 2 years ago
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    3 log 2 x + 1/2 log 2 y – 3 log 2 z = log 2 (x^3√y / z^3).

  3. ParthKohli
    • 2 years ago
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    Nothing is impossible.

  4. ParthKohli
    • 2 years ago
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    Okay, that's an impossible equation indeed. But it has multiple solutions.

  5. vivalakoda
    • 2 years ago
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    Exaggeration of course, ha

  6. vivalakoda
    • 2 years ago
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    So it is capable of being solved? I could call it true?

  7. ParthKohli
    • 2 years ago
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    Yes, it can be solved by using these identities:\[\log_a b + \log _a c = \log_a (bc)\]and\[\log_a b - \log_a c = \log_a (b/c)\]

  8. jiteshmeghwal9
    • 2 years ago
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    \[\log_2x^3+\log_2y^{1/2}-\log_2z^3=\log_2(x^3\sqrt{y}/z^3)\]

  9. ParthKohli
    • 2 years ago
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    Two more:\[a\log b = \log b^a\]and\[\log_a b = \log_a c \iff b = c\]

  10. jiteshmeghwal9
    • 2 years ago
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    now i think it's possible now

  11. ParthKohli
    • 2 years ago
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    I am very, very lazy and I am very, very serious about that. So I think @jiteshmeghwal9 will continue helping :-p

  12. jiteshmeghwal9
    • 2 years ago
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    o_O

  13. vivalakoda
    • 2 years ago
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    It asks me if the equation is true, and if so then to explain the properties used. o.o

  14. ParthKohli
    • 2 years ago
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    The identities I listed.

  15. ParthKohli
    • 2 years ago
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    Use them one-by-one.

  16. jiteshmeghwal9
    • 2 years ago
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    \(log_2x^3+log_2(y^{1/2})=log_2(x^3\sqrt{y})\) now \(log_2(x^3\sqrt{y})-log_2z^3=log_2(x^3\sqrt{y}/z^3)\)

  17. ParthKohli
    • 2 years ago
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    That's it, right there. ^

  18. jiteshmeghwal9
    • 2 years ago
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    \[\log_2x^3+\log_2y^{1/2}-\log_2z^3=\log_2(x^3\sqrt{y}/z^3)\]since\[\log_2x^3+\log_2(y^{1/2})=\log_2(x^3\sqrt{y})\]\[\log_2(x^3\sqrt{y})-\log_2z^3=\log_2(x^3\sqrt{y}/z^3)\]so,\[\log_2(x^3\sqrt{y}/z^3)=\log_2(x^3\sqrt{y}/z^3)\]H.P.

  19. ParthKohli
    • 2 years ago
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    Brotip: Use Q.E.D. instead of H.P. :-)

  20. jiteshmeghwal9
    • 2 years ago
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    Q.E.D=?

  21. vivalakoda
    • 2 years ago
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    I am so confused. Thank you everyone for the help, I'll just do my best to take the identities you both listed and write something about it. Very much appreciated!

  22. jiteshmeghwal9
    • 2 years ago
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    yw :) Best of luck;)

  23. vivalakoda
    • 2 years ago
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    By properties they mean the logarithmic properties :c I just asked my teacher. So the power property, the product property, and the quotient property? Would any of those fit?

  24. AravindG
    • 2 years ago
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    Power Property \[\log a^b=b \log a\] Product Property \[\log ab= \log a +\log b \] Quotient property \[\log \dfrac{a}{b}=\log a - \log b\]

  25. jiteshmeghwal9
    • 2 years ago
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    \(blog_ac=log_ac^b\) \(log_ab+log_ac=log_abc\) \(log_ab - log_ac=log_a\dfrac{b}{c}\)

  26. jiteshmeghwal9
    • 2 years ago
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    these are the only properties used in the question

  27. vivalakoda
    • 2 years ago
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    How do they show that the equation is true, though?

  28. jiteshmeghwal9
    • 2 years ago
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    I have proved this above

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