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$${{\mathtt{5}}}^{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}\right)} = {\mathtt{104}} \Rightarrow {{\mathtt{5}}}^{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)} = {\mathtt{104}}{\mathtt{\,-\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}\right)} \Rightarrow {{\mathtt{5}}}^{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)} = {\mathtt{104}}{\mathtt{\,-\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}\right)}$$

Guest Aug 15, 2015

Best Answer 

 #3
avatar+17652 
+10

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

2x + 1 + 5·2x - 2 = 104   

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

geno3141  Aug 15, 2015
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5+0 Answers

 #1
avatar+26322 
+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.

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

.

Alan  Aug 15, 2015
 #2
avatar
+5

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

Guest Aug 15, 2015
 #3
avatar+17652 
+10
Best Answer

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

2x + 1 + 5·2x - 2 = 104   

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

geno3141  Aug 15, 2015
 #4
avatar+26322 
+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

.

Alan  Aug 16, 2015
 #5
avatar+90970 
+5

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 

 

2x + 1 + 5·2x - 2 = 104 

then 

 

2x + 1 + 5·2x - 2 - 104 =0

If we graph 

y=2x + 1 + 5·2x - 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.

Melody  Aug 16, 2015

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