5^(x+1)+5*2^(x-2)=104, x=5

To get the answer of 5, change the first '5' into a '2':

2^{x + 1} + 5·2^{x - 2} = 104   

If you graph the function  y  =  2^{x + 1} + 5·2^{x - 2} - 104, you will get the solution  x = 5. 

If you want to solve the equation look at http://web2.0calc.com/questions/5-x-1-5-2-x-2-104 

Evaluating the left-hand side of the equation at x = 5 does not result in 104.

$${{\mathtt{5}}}^{\left({\mathtt{5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{\left({\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{2}}\right)} = {\mathtt{15\,665}}$$

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Exponential Equations, I only know that result is x=5

Well spotted geno!

2^(x+1) + 5*2^(x-2) = 104

2^x*(2 + 5/4) = 104

2^x*13/4 = 104

2^x = 104*4/13

2^x = 32

2^x = 2^5

x = 5

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I understand both answers but I do not understand this statement Geno

To get the answer of 5, change the first '5' into a '2'  

(Sorry I get you now - how on Earth did you figure that out!)

What does that mean and what has it got to do with your graphical solution ?

Your algebra is really neat Alan  

Geno has said that if 

2^{x + 1} + 5·2^{x - 2} = 104 

then 

2^{x + 1} + 5·2^{x - 2} - 104 =0

If we graph 

y=2^{x + 1} + 5·2^{x - 2} - 104 

and we graph

y=0    (this is just the x axis)

then, where the two graphs cross on the x axis will be the solution.

This is a technique that we use all the time but I think many students (even those who use it ) do not really understand what they are doing. :)

Here is the graph.