#1**+5 **

First draw a graph to see the likely value.

Looks like it might be x = -2.

Try x=2

-2+6 = 4

0.5^{-2} = 1/2^{-2} = 2^{2} = 4

So x = 2.

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

Take log_{2} 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

#1**+5 **

Best Answer

First draw a graph to see the likely value.

Looks like it might be x = -2.

Try x=2

-2+6 = 4

0.5^{-2} = 1/2^{-2} = 2^{2} = 4

So x = 2.

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

Take log_{2} 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