katherinesmith
  • katherinesmith
what is the range of this function?
Mathematics
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SOLVED
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chestercat
  • chestercat
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katherinesmith
  • katherinesmith
what is the range of the function \[y = 2^{x + 3} - 3\]
anonymous
  • anonymous
does it help to know that \(2^x>0\) always ?
anonymous
  • anonymous
when x goes to minus infinity y goes to -3, but never reach it also when x goes to infinity y also goes to it , so the range is (-3,infinity)

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katherinesmith
  • katherinesmith
thank you @ahmad1 could you help me with another?
anonymous
  • anonymous
bring it :)
katherinesmith
  • katherinesmith
how do i find the solution of \[(2.4)^{x} = 9\]
anonymous
  • anonymous
take log 2.4 for both sides to find that \[x= \log_{2.4}9 \]
anonymous
  • anonymous
but you will have a small problem in the MCQS if it's one of them ,is it?
katherinesmith
  • katherinesmith
MCQS?
anonymous
  • anonymous
multiple choices question
katherinesmith
  • katherinesmith
it's a true or false question, the question is whether or not the solution is approximately 3.75
anonymous
  • anonymous
I think this is far away of being an answer to me :\ \[2.4^{3.75}=\frac{ 24^{3.75} }{ 10^{3.75} }\] is not too close to 9 in my opinion , it's about 25 actually
katherinesmith
  • katherinesmith
thanks for the help, i'll just put false
anonymous
  • anonymous
you are welcome :)
anonymous
  • anonymous
\[2.4^x=9\iff x=\frac{\ln(9)}{\ln(2.4)}\] and a calculator

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