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anonymous

  • one year ago

Find the exact solution to the equation. 320(1/4)^x/4=5

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  1. anonymous
    • one year ago
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    @Directrix

  2. campbell_st
    • one year ago
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    you'll need logs start by dividing both sides of the equation by 320 then take the log of both sides then apply the log laws for powers... does that make sense..?

  3. anonymous
    • one year ago
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    i dont undetstand taking the log of both sides

  4. campbell_st
    • one year ago
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    ok... so if you divide both sides by 320 you get \[(\frac{1}{4})^{\frac{x}{4}} = \frac{5}{320}\] does that make sense...?

  5. anonymous
    • one year ago
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    yes i understand that part

  6. campbell_st
    • one year ago
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    ok... so take the natural log of both sides or you can look at it this way \[(\frac{1}{4})^\frac{x}{4} = \frac{5}{320}~~~~or~~~~(\frac{1}{4})^{\frac{x}{4}} = \frac{1}{64}\] does that make sense...?

  7. anonymous
    • one year ago
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    im sorry but i dont understand what you mean take the natural log

  8. campbell_st
    • one year ago
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    well if you want to do the solution with logs you can... but what I have posted is an alternate method. using Logarithms is the most obvious method... but using the alternate method you have \[(\frac{1}{4})^\frac{x}{4} = \frac{1}{64}\] so write the right hand side of the equation as a power with a base of 1/4

  9. campbell_st
    • one year ago
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    then you get \[(\frac{1}{4})^{\frac{x}{4}} = (\frac{1}{4})^3\] now you have the same base, you can equate the powers and solve for x.

  10. anonymous
    • one year ago
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    x=12?

  11. campbell_st
    • one year ago
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    that's it... you can check by substituting into the original equation

  12. anonymous
    • one year ago
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    thank you so much

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