Question 941182
<pre>
{{{4^(x+1)}}}{{{""=""}}}{{{(1/2)^(-x)}}}

We want to get both sides to an exponential with the same base.
replace 4 by {{{2^2}}} and on the right flip the fraction
and change the sign of the exponent to positive.

{{{(2^2)^(x+1)}}}{{{""=""}}}{{{2^x}}}

Multiply the exponents on the left

{{{2^(2(x+1))}}}{{{""=""}}}{{{2^x}}}

Now the base of the exponentials on both sides are the
same positive number (not 1).  So we can equate the
exponents:  

{{{2(x+1)}}}{{{""=""}}}{{{x}}}

Distribute on the left

{{{2x+2}}}{{{""=""}}}{{{x}}}

Add -2 to both sides

{{{2x}}}{{{""=""}}}{{{x-2}}}

Add -x to both sides

{{{x}}}{{{""=""}}}{{{-2}}}

Edwin</pre>