## MasterMindXD 3 years ago solve 2log(x+11)=(1/2)^x.

1. Ishaan94

what's log's base?

2. MasterMindXD

10

3. Ishaan94

Oh okay...

4. Ishaan94

$2\log (x+ 11) = \left( \frac{1}{2}\right)^x$

5. Ishaan94

that is the question right?

6. MasterMindXD

Yeah, let me show you what I've got so far.

7. MasterMindXD

|dw:1324553869100:dw|

8. 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

9. MasterMindXD

How do I continue from this?

10. 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<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 ...

11. MasterMindXD

How did you find out that they meet at -1? What is the method you used to figure that out?

12. 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 ...

13. MasterMindXD

Oh okay, I'll try that. Thank you :D

14. cristiann

You are welcome ... :)

15. arijit.mech

16. cristiann

Seems to be another equation? (an extra x on the left-hand side?)