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Exponential inequalities
10-17-2015, 09:06 AM
Post: #9
RE: Exponential inequalities
(10-11-2015 10:20 AM)Aries Wrote:  
(10-10-2015 11:58 AM)parisse Wrote:  The solver can solve polynomial-like equations/inequations. Unfortunately there is no easy way to reduce all equations/inequations to a polynomial. But most of the time, you can help the CAS by calling the right pre-simplification command. Here you can do
a:=tsimplify(2^(3*x-1)+2^(6*x-2)-2^(3*x+3)-(4^(3*x-2))
This will express the inequation in terms of the minimum possible independant "variables", here 1, hence the inequation becomes polynomial-like, then
solve(a<0)
will return the exact answer.
The approx answer is partially wrong because the floats are too small for x negative.
Remember: the calc computes very fast but it is stupid, humans do not compute fast but humans know what to do, a typical situation where both can cooperate!

Thank you, parisse, calling "tsimplify" does really work fine:

[Image: th_543688154_disespon_122_183lo.jpg]

However, why that "equal" sign in the solution ? O_o

(2^(3*x))/2+(2^(6+x))/4-2^(3*x)*8-(2^(6*x))/16<0; ((2^(6*x)*(4-1))/16)+((2^(3*x)*(1-16))/2)<0; setting (2^(3*x))=u, we've got (3/16)*(u^2)-(15/2)*u<0.
Doing lcm, we've got (u^2)-40*u<0, then u*(u-40)<0.
u<0 is never verified (2^(3*x)<0).
Doing u<40, we've got ln(2^(3*x))<ln(40) and finally x<(ln(5)+ln(8))/ln(8).
I'm wondering why that "equal" sign in the Prime result *_*
Best,

Aries ;-)
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Messages In This Thread
Exponential inequalities - Aries - 10-09-2015, 10:54 AM
RE: Exponential inequalities - roadrunner - 10-10-2015, 10:35 AM
RE: Exponential inequalities - parisse - 10-10-2015, 11:58 AM
RE: Exponential inequalities - Aries - 10-11-2015, 10:20 AM
RE: Exponential inequalities - Aries - 10-17-2015 09:06 AM
RE: Exponential inequalities - Tim Wessman - 10-10-2015, 01:54 PM
RE: Exponential inequalities - Aries - 10-11-2015, 06:39 AM
RE: Exponential inequalities - roadrunner - 10-10-2015, 11:03 PM
RE: Exponential inequalities - Aries - 10-11-2015, 10:23 AM
RE: Exponential inequalities - parisse - 10-17-2015, 04:15 PM
RE: Exponential inequalities - Aries - 10-25-2015, 10:53 AM



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