How do you solve for x: in $2^x + 2^-x = 5/2$ ?

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Answer 1 · 2016-05-14T20:50:30

$x=+-1$

(I'm hoping that someone will come up with a better method of solving, since the following is simply "solution by observation").

We are told: $2^x+2^(-x)=5/2$

Observe that
$color(white)("XXXX")5/2 = 4/2 + 1/2$

$color(white)("XXXXX")=2 + 1/2$

$color(white)("XXXXX")=2^1+1/2^1$

$color(white)("XXXXX")=2^1+2^(-1)$

So $2^x+2^(-x)=2^1+2^(-1) =2^-1+2^1$
which implies

$color(white)("XXX")x=+-1$

Graph

Another possible way is looking at a graph

Graph for #2^x+2^(-x)#

How do you solve for x: in 2^x + 2^-x = 5/22^x + 2^-x = 5/2?