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solve for x: x+6=.5^x

 May 23, 2014

Best Answer 

 #1
avatar+30397 
+5

First draw a graph to see the likely value.

2x

Looks like it might be x = -2.

Try x=2

 -2+6 = 4

0.5-2 = 1/2-2 = 22 = 4

So x = 2.

If you prefer a numerical approach rewrite the equation as 2x = 1/(x+6)

Take log2 of both sides

x = log2(1/(x+6))  ...(1)

Make an initial guess for x, say x = -1.  Plug this into the right-hand side of equation (1) to get a new estimate for x. Plug this new value into the right-hand side of equation (1) to get yet another estimate, and so on.  Repeat until you converge on a unique value.  In this case the process will converge on the number -2 in 9 or 10 iterations. 

 May 23, 2014
 #1
avatar+30397 
+5
Best Answer

First draw a graph to see the likely value.

2x

Looks like it might be x = -2.

Try x=2

 -2+6 = 4

0.5-2 = 1/2-2 = 22 = 4

So x = 2.

If you prefer a numerical approach rewrite the equation as 2x = 1/(x+6)

Take log2 of both sides

x = log2(1/(x+6))  ...(1)

Make an initial guess for x, say x = -1.  Plug this into the right-hand side of equation (1) to get a new estimate for x. Plug this new value into the right-hand side of equation (1) to get yet another estimate, and so on.  Repeat until you converge on a unique value.  In this case the process will converge on the number -2 in 9 or 10 iterations. 

Alan May 23, 2014

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