Exponential inequalities
10-17-2015, 09:06 AM
Post: #9
 Aries Member Posts: 159 Joined: Oct 2014
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)
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:

(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).