## MasterMindXD 3 years ago How to solve 10^[(10^(x+11)) +(0.5^(x+11))] =0

1. Ishaan94

not possible i don't think a^(n) = 0 is possible

2. MasterMindXD

Well, this is what I had before....log(log(x+11))=log^((1/2)^(x+11)).

3. Ishaan94

oh okay

4. Ishaan94

log^((1/2)^(x+11))??

5. MasterMindXD

yeah

6. Ishaan94

i am assuming it's $\log_{10} \log_{10} (x+11) = \log_{10} \frac{1}{2^{x+ 11}}$

7. MasterMindXD

okay yeah...

8. cristiann

The equation log(x+11)=((1/2))^{x+11} has a unique solution, which cannot be found exactly (or guessed ... :) ) The existence is proved by Darboux-type reasoning: for x=-10: log1=0<(1/2)^1=1/2 for x=-1: log10=1>(1/2)^10 Unicity is proven by monotonicity ... :)

9. cristiann

The unique solution may be found numerically to be x=-9.5559 Darboux-type reasoning refers to: f(x1)<0 and f(x2)>0 and f() continuous then there is at least one value x0 between x1 and x2 such that f(x0)=0

10. cristiann

:)

11. Ishaan94

wow cristiann, you're awesome at mathematics

12. cristiann

Thanks ... not really ... just older ... :)

13. cristiann

And I'm taking you all the fun of doing them ...:)

14. arijit.mech