anonymous
  • anonymous
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
50^x
Kash_TheSmartGuy
  • Kash_TheSmartGuy
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.
anonymous
  • anonymous
i saw that on yahoo answers but i dont think my teacher would like the trial and error part

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anonymous
  • anonymous
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)
anonymous
  • anonymous
@dan815
anonymous
  • anonymous
and for the first one there's the equal bases part
anonymous
  • anonymous
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
`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 \[\large 2^x = 10 \implies x = \log_{\ 2}(10) = \frac{\log(10)}{\log(2)} \approx 3.3219\]
jim_thompson5910
  • jim_thompson5910
I used the change of base formula to get the approximate decimal form
anonymous
  • anonymous
so would i write x=log50(17)
jim_thompson5910
  • jim_thompson5910
yeah \[\LARGE x = \log_{50}(17)\] then you use the change of base formula to get the approximate value of x
anonymous
  • anonymous
0.724
jim_thompson5910
  • jim_thompson5910
Rules: \[\Large b^x = y \rightarrow x = \log_b(y)\] Change of base formula \[\Large \log_{b}\left(x\right)=\frac{\log\left(x\right)}{\log\left(b\right)}\]
jim_thompson5910
  • jim_thompson5910
I'm getting 0.724 as well
jim_thompson5910
  • jim_thompson5910
so that means \[\LARGE 50^{0.724} \approx 17\]
anonymous
  • anonymous
yay thanks! what about the second part? like if the bases were equal
jim_thompson5910
  • jim_thompson5910
if the bases are equal, then you can set the exponents equal and solve for x
anonymous
  • anonymous
thanks so much you're the best! Dan who??
jim_thompson5910
  • jim_thompson5910
example \[\Large 2^3 = 2^{x+1}\] the bases are both 2, so the exponents must be equal therefore, 3 = x+1
anonymous
  • anonymous
ohh okay i get it
anonymous
  • anonymous
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)
jim_thompson5910
  • jim_thompson5910
by " f-1(x)" you mean \(\LARGE f^{-1}(x)\) right?
anonymous
  • anonymous
yes
jim_thompson5910
  • jim_thompson5910
what does that notation mean? any ideas?
anonymous
  • anonymous
no i dont understand it
jim_thompson5910
  • jim_thompson5910
it means "inverse function of f"
jim_thompson5910
  • jim_thompson5910
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
anonymous
  • anonymous
so it can be found depending on what has been done?
anonymous
  • anonymous
so would f-1(132) be 132
anonymous
  • anonymous
-132
jim_thompson5910
  • jim_thompson5910
what undoes exponents?
anonymous
  • anonymous
LOGS
anonymous
  • anonymous
YOU TAUGHT ME THAT
jim_thompson5910
  • jim_thompson5910
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
anonymous
  • anonymous
so for what it means would i just write it means the inverse of 132? or the inverse of f of 132?
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
why is this important? because we can use the inverse to answer questions like "in what year will the number of shoes be 132?"
anonymous
  • anonymous
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?
jim_thompson5910
  • jim_thompson5910
yeah
anonymous
  • anonymous
yaya thankyouuuu
jim_thompson5910
  • jim_thompson5910
|dw:1436396943396:dw|
anonymous
  • anonymous
jim you're so nice!
jim_thompson5910
  • jim_thompson5910
|dw:1436396954380:dw|
anonymous
  • anonymous
and you're patient and good at explaining things
anonymous
  • anonymous
thanks so much
jim_thompson5910
  • jim_thompson5910
no problem

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