anonymous
  • anonymous
solve 2log(x+11)=(1/2)^x.
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
what's log's base?
anonymous
  • anonymous
10
anonymous
  • anonymous
Oh okay...

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anonymous
  • anonymous
\[2\log (x+ 11) = \left( \frac{1}{2}\right)^x\]
anonymous
  • anonymous
that is the question right?
anonymous
  • anonymous
Yeah, let me show you what I've got so far.
anonymous
  • anonymous
|dw:1324553869100:dw|
cristiann
  • cristiann
First observe that x=-1 is a solution. Then use the monotonicity of the functions log and exponent (with subunitary base) to proove that this solution is unique
anonymous
  • anonymous
How do I continue from this?
cristiann
  • cristiann
Consider two functions: f1(x)=2log(x+11) and f2(x)=(1/2)^x. At x=-1 they meet for x>-1, f1 increases (is above) and f2 decreases (is below), so they don't meet anymore... for -11
anonymous
  • anonymous
How did you find out that they meet at -1? What is the method you used to figure that out?
cristiann
  • cristiann
No method ... just by trial and error ... you should always check for some common values ... just to see how it behaves ... this is a prefabricated exercise .... so it should have some easy values to be guessed ... for a real/life situation ... you have to apply numerical methods (which anyway are not sure...) and combine them with some reasoning ...
anonymous
  • anonymous
Oh okay, I'll try that. Thank you :D
cristiann
  • cristiann
You are welcome ... :)
anonymous
  • anonymous
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cristiann
  • cristiann
Seems to be another equation? (an extra x on the left-hand side?)

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