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

1. Ishaan94 Group Title

what's log's base?

2. MasterMindXD Group Title

10

3. Ishaan94 Group Title

Oh okay...

4. Ishaan94 Group Title

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

5. Ishaan94 Group Title

that is the question right?

6. MasterMindXD Group Title

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

7. MasterMindXD Group Title

|dw:1324553869100:dw|

8. cristiann Group Title

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 Group Title

How do I continue from this?

10. cristiann Group Title

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 Group Title

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

12. cristiann Group Title

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 Group Title

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

14. cristiann Group Title

You are welcome ... :)

15. arijit.mech Group Title

16. cristiann Group Title

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