SOLUTION: Good evening (Happy New Year to you all!!) Has somebody the patience to explain me step by step the solution of this exp.equation:? 4^(x-3)+2^(13-2x)=24 Results should be: x=9

Question 1012127: Good evening (Happy New Year to you all!!)
Has somebody the patience to explain me step by step the solution of
this exp.equation:? 4^(x-3)+2^(13-2x)=24
Results should be: x=9/2 or x=5
Thank you very much in advance

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
4^(x-3)+2^(13-2x)=24
4 = 2^2

Sub u for 2^2x

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=262144 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1024, 512. Here's your graph:

=================

2x = 10
x = 5
--------------------------

x = 9/2

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