Question 169003
Solve for x:
{{{2^(x+1)*8^(-x) = 4}}} Substitute {{{8 = 2^3}}} and {{{4 = 2^2}}}
{{{2^(x+1)*2^(-3x) = 2^2}}} Perform the indicated multiplication by adding the exponents.
{{{2^(x+1-3x) = 2^2}}} Simplify the left side.
{{{2^(1-2x) = 2^2}}} The bases (2) are equal so the exponents are equal.
{{{1-2x = 2}}} Subtract 1 from both sides.
{{{-2x = 1}}} Divide both sides by -2.
{{{highlight(x = -1/2)}}} 
Check:
{{{2^(x+1)*8^(-x) = 4}}} Substitute {{{x = -1/2}}}
{{{2^(-(1/2)+1)*8^(-(-1/2)) = 4}}} Substitute {{{8 = 2^3}}} and simplify the left side.
{{{2^(1/2)*2^(3/2) = 4}}} Perform the indicated multiplication by adding the exponents.
{{{2^(4/2) = 4}}} 
{{{2^2 = 4}}}
{{{4 = 4}}}