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Ishaan94Best ResponseYou've already chosen the best response.0
\[2\log (x+ 11) = \left( \frac{1}{2}\right)^x\]
 2 years ago

Ishaan94Best ResponseYou've already chosen the best response.0
that is the question right?
 2 years ago

MasterMindXDBest ResponseYou've already chosen the best response.0
Yeah, let me show you what I've got so far.
 2 years ago

MasterMindXDBest ResponseYou've already chosen the best response.0
dw:1324553869100:dw
 2 years ago

cristiannBest ResponseYou've already chosen the best response.2
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
 2 years ago

MasterMindXDBest ResponseYou've already chosen the best response.0
How do I continue from this?
 2 years ago

cristiannBest ResponseYou've already chosen the best response.2
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<x<1, f1 is below and f2 is above, so they again don't meet. So, a unique meeting point ....1 How can you find the point 1? Just by geuessing ... no procedure for finding it ...
 2 years ago

MasterMindXDBest ResponseYou've already chosen the best response.0
How did you find out that they meet at 1? What is the method you used to figure that out?
 2 years ago

cristiannBest ResponseYou've already chosen the best response.2
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 ...
 2 years ago

MasterMindXDBest ResponseYou've already chosen the best response.0
Oh okay, I'll try that. Thank you :D
 2 years ago

cristiannBest ResponseYou've already chosen the best response.2
You are welcome ... :)
 2 years ago

cristiannBest ResponseYou've already chosen the best response.2
Seems to be another equation? (an extra x on the lefthand side?)
 2 years ago
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