Question 701470
Without using a calculator, solve for x:
a) {{{8^x = 1/sqrt(2)}}}
Write the square root as an exponent
{{{8^x = 1/2^(1/2)}}}
CAn also be written
{{{8^x = 2^(-1/2)}}}
8 can be written as 2^3
{{{2^(3x) = 2^(-1/2)}}}
therefore
3x = {{{-1/2}}}
x = {{{-1/2}}}*{{{1/3}}}
x = {{{-1/6}}}


b) {{{4^((2x+1)) = (1/2)^((2-x))}}}
we can rewrite this to
{{{2^(2(2x+1)) = 2^(-(2-x))}}}
{{{2^((4x+2)) = 2^((x-2))}}}
therefore
4x + 2 = x - 2
4x - x = -2 - 2
3x = -4
x = {{{-4/3}}}