SOLUTION: Solve 24(2²ˣ) - 5(2ˣ⁺²)

SOLUTION: Solve 24(2²ˣ) - 5(2ˣ⁺²) - 156 = 0, where x ∈ R

Question 1210448: Solve 24(2²ˣ) - 5(2ˣ⁺²) - 156 = 0, where x ∈ R

Answer by ikleyn(53354) (Show Source): You can put this solution on YOUR website!
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Solve 24(2²ˣ) - 5(2ˣ⁺²) - 156 = 0, where x ∈ R
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This given equation

     -    - 156  =  0    (1)


is the same as

      -    -  156  =  0,

or

     -  -  156  =  0.    (2)


Introduce new variable  y = .


Then equation (2)  takes the form

     -  - 156 = 0,

and we are looking for positive solutions to this equation.


Apply the quadratic formula and get the solutions to equation (2)

    y = 3  and  y = -13/6.


Only positive solution y = 3 does fit.


So, for x we have

     = 3,   hence,  x =  = 1.584962501  (approximately).


ANSWER.  x =  = 1.584962501  (approximately).

Solved.

This is a standard problem to solve exponential equation by introducing new variable.

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