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Math Help - Exponents and Log Help!!

  1. #1
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    Exponents and Log Help!!

    I have four problems I need help on:
    5a^2/3*4a^3/2
    (I believe it's multiplying, the copier messed up)
    4a^5/3^3/2

    log5(3x+1)=2
    (It's log Base 5, as in the 5 there should be below the rest of the equation)

    Log5x(x-1)=2
    (This is base 10)
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  2. #2
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    Re: Exponents and Log Help!!

    Do you have to simplify the exercice(s) with the exponents?

    For the logarithmic equations, use: \log_a(x)=y \Leftrightarrow a^y=x
    For example the second one:
    \log_5(3x+1)=2 \Leftrightarrow 5^2=3x+1 \Leftrightarrow ...
    (and offcourse if you want to do the solution check: 3x+1>0)
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    Re: Exponents and Log Help!!

    what you wants solution or simplification
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  4. #4
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    Re: Exponents and Log Help!!

    I have to simplify and evaluate.
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  5. #5
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    Re: Exponents and Log Help!!

    Then you've to know the basic rules like for example a^{x}\cdot a^{y}=a^{x+y}, ... .
    Can you continue with the hint I gave about the logarithmic equations?

    Try to do some work by yourself, that's the best way to learn something.
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  6. #6
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    Re: Exponents and Log Help!!

    I did the first one very fast, but for the second one, how does the 5x affect the rule? Because I guess it would be 100 = 5x(x-1)
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  7. #7
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    Re: Exponents and Log Help!!

    If the equation is:
    \log[5x\cdot(x-1)]=2 then indeed 100=5x(x-1)\Leftrightarrow ... .

    What about the exercice with the exponents?
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  8. #8
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    Re: Exponents and Log Help!!

    I solved the second one by creating a quadratic and bringing everything to one side before factoring. I came up with 5(x-5)(x+4)
    Now, I have to figure out the exponents.
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  9. #9
    MHF Contributor Siron's Avatar
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    Re: Exponents and Log Help!!

    Right! x=-4 and x=5 are indeed the solutions (don't forget to check them!)

    But your first exercice is not clear, because you're not using brackets.
    I guess you've to simplify:
    \frac{5a^2}{3}\cdot \frac{4a^3}{2}
    (to simplify, look at the 'basic rule' I gave in one of my previous posts)
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  10. #10
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    Re: Exponents and Log Help!!

    For the question: 4a^5/3^3^2, is there some way I can combine both exponents into one fraction?
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  11. #11
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    Re: Exponents and Log Help!!

    Thanks for the rules, I will have to remember them! So, again, for the first one:
    If I combine the two fractions:
    I came up with
    20a^10/6

    After this, would the answer come out to 10a^10/3
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  12. #12
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    Re: Exponents and Log Help!!

    If the exercice is:
    5a^{\frac{2}{3}}\cdot 4a^{\frac{3}{2}}=20a^{\frac{2}{3}+\frac{3}{2}}=20a  ^{\frac{13}{6}}

    Now the second one, can you be more clear with using brackets?
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  13. #13
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    Re: Exponents and Log Help!!

    How does it come out to 13/6?

    And, the question is:
    4a^{\frac{5}{3}^{\frac{3}{2}
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  14. #14
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    Re: Exponents and Log Help!!

    Because:
    \frac{3}{2}+\frac{2}{3}=\frac{9+4}{6}=\frac{13}{6}
    For the second one you can use this 'basic rule':
    (a^{x})^{y}=a^{x\cdot y}
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  15. #15
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    Re: Exponents and Log Help!!

    So, I got
    32(a^{\frac{5}{2})

    And, for the top part, you cross-multiplied both ways and added them both?
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