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anonymous

  • one year ago

Erika was working on solving the exponential equation 50x = 17; however, she is not quite sure where to start. Using complete sentences, describe to Erika how to solve this equation and how solving would be different if the bases were equal. (10 points)

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  1. anonymous
    • one year ago
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    50^x

  2. Kash_TheSmartGuy
    • one year ago
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    Erika could solve with a calculator and do trial and error until she found some power of 5 that would equal 17 (it's a little above 1.76 by this method). But being a smart person, Erika would see that the best solution would be to take logs of both sides Log 5^x = log 17....... Erika knows that log 5^x = x(log 5) x(log 5) = log 17 0.69897x = 1.2304489....divide across by 0.69897 x = 1.76055, a much more precise solution With the above you can surely write a few sentences.

  3. anonymous
    • one year ago
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    i saw that on yahoo answers but i dont think my teacher would like the trial and error part

  4. anonymous
    • one year ago
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    It's ok ill use that for that question but how about this one Brett has determined a function f(x) that shows the exponential growth of the number of shoes Larae owns each year. Explain how the f-1(x) can be found and what f-1(132) means. (10 points)

  5. anonymous
    • one year ago
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    @dan815

  6. anonymous
    • one year ago
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    and for the first one there's the equal bases part

  7. anonymous
    • one year ago
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    @jim_thompson5910

  8. jim_thompson5910
    • one year ago
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    `Erika was working on solving the exponential equation` \(\LARGE 50^x = 17\) `; however, she is not quite sure where to start. Using complete sentences, describe to Erika how to solve this equation and how solving would be different if the bases were equal.` use logs to isolate exponents example \[\large 2^x = 10 \implies x = \log_{\ 2}(10) = \frac{\log(10)}{\log(2)} \approx 3.3219\]

  9. jim_thompson5910
    • one year ago
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    I used the change of base formula to get the approximate decimal form

  10. anonymous
    • one year ago
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    so would i write x=log50(17)

  11. jim_thompson5910
    • one year ago
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    yeah \[\LARGE x = \log_{50}(17)\] then you use the change of base formula to get the approximate value of x

  12. anonymous
    • one year ago
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    0.724

  13. jim_thompson5910
    • one year ago
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    Rules: \[\Large b^x = y \rightarrow x = \log_b(y)\] Change of base formula \[\Large \log_{b}\left(x\right)=\frac{\log\left(x\right)}{\log\left(b\right)}\]

  14. jim_thompson5910
    • one year ago
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    I'm getting 0.724 as well

  15. jim_thompson5910
    • one year ago
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    so that means \[\LARGE 50^{0.724} \approx 17\]

  16. anonymous
    • one year ago
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    yay thanks! what about the second part? like if the bases were equal

  17. jim_thompson5910
    • one year ago
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    if the bases are equal, then you can set the exponents equal and solve for x

  18. anonymous
    • one year ago
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    thanks so much you're the best! Dan who??

  19. jim_thompson5910
    • one year ago
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    example \[\Large 2^3 = 2^{x+1}\] the bases are both 2, so the exponents must be equal therefore, 3 = x+1

  20. anonymous
    • one year ago
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    ohh okay i get it

  21. anonymous
    • one year ago
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    what about for the brett problem? Brett has determined a function f(x) that shows the exponential growth of the number of shoes Larae owns each year. Explain how the f-1(x) can be found and what f-1(132) means. (10 points)

  22. jim_thompson5910
    • one year ago
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    by " f-1(x)" you mean \(\LARGE f^{-1}(x)\) right?

  23. anonymous
    • one year ago
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    yes

  24. jim_thompson5910
    • one year ago
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    what does that notation mean? any ideas?

  25. anonymous
    • one year ago
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    no i dont understand it

  26. jim_thompson5910
    • one year ago
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    it means "inverse function of f"

  27. jim_thompson5910
    • one year ago
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    the inverse undoes whatever operation was applied so say you add initially, the inverse would be subtraction if you multiply, the inverse is division if you square something, the inverse is the square root

  28. anonymous
    • one year ago
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    so it can be found depending on what has been done?

  29. anonymous
    • one year ago
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    so would f-1(132) be 132

  30. anonymous
    • one year ago
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    -132

  31. jim_thompson5910
    • one year ago
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    what undoes exponents?

  32. anonymous
    • one year ago
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    LOGS

  33. anonymous
    • one year ago
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    YOU TAUGHT ME THAT

  34. jim_thompson5910
    • one year ago
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    yes you will use logs to get the inverse of f we can't actually find the inverse since we don't know what the function f is

  35. anonymous
    • one year ago
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    so for what it means would i just write it means the inverse of 132? or the inverse of f of 132?

  36. jim_thompson5910
    • one year ago
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    the original f(x) function takes an x value, which is the number of years, and produces a y value y = f(x) in goes x ----> out comes y or f(x) x = number of years y = number of shoes

  37. jim_thompson5910
    • one year ago
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    the inverse takes everything in reverse because we're undoing everything with the inverse, the y value is now the input, the x is the output in goes y into the inverse ----> out comes x

  38. jim_thompson5910
    • one year ago
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    why is this important? because we can use the inverse to answer questions like "in what year will the number of shoes be 132?"

  39. anonymous
    • one year ago
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    so it would be right if i wrote that f-1(132) means that you take the inverse of it and now the y value is the input and the x is the output?

  40. jim_thompson5910
    • one year ago
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    yeah

  41. anonymous
    • one year ago
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    yaya thankyouuuu

  42. jim_thompson5910
    • one year ago
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    |dw:1436396943396:dw|

  43. anonymous
    • one year ago
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    jim you're so nice!

  44. jim_thompson5910
    • one year ago
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    |dw:1436396954380:dw|

  45. anonymous
    • one year ago
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    and you're patient and good at explaining things

  46. anonymous
    • one year ago
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    thanks so much

  47. jim_thompson5910
    • one year ago
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    no problem

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