Question 554298
Solve for x:
{{{(2^x)*(8^(x+1)) = 16^(1/3)}}} Replace: {{{8 = 2^3}}} and {{{16 = 2^4}}}
{{{(2^x)*(2^3)^(x+1) = 2^(4(1/3))}}} Simplify.
{{{(2^x)*(2^(3x+3)) = 2^(4/3)}}} Add the exponents on the left side.
{{{2^(4x+3) = 2^(4/3)}}} Since the bases (that's 2) are equal, the exponents are equal, so...
{{{4x+3 = 4/3}}} Multiply through by 3 to clear the fraction.
{{{12x+9 = 4}}} Subtract 9 from both sides.
{{{12x = -5}}} Divide by 12.
{{{x = -5/12}}}
Check:
{{{(2^x)*(8^(x+1)) = 16^(1/3)}}} Substitute x = -5/12
{{{2^(-5/12)*(8^(7/12)) = 16^(1/3)}}}
{{{2^(5/12)*(2^(21/12)) = 2^(4/3)}}} Simplify.
{{{(2^(21/12))/(2^(5/12)) = 2^(4/3)}}}
{{{2^(16/12) = 2^(4/3)}}}
{{{2^(4/3) = 2^(4/3)}}}