Question 11161
1. {{{64^x = 8}}}, well short of doing logs or knowing the answer by looking, as i would expect someone who is 17-18 years old to do (i have no idea how old you are), then do the following:


{{{(2^6)^x = 2^3}}}
{{{2^(6x) = 2^3}}}


so, the two sides are equal, so 6x = 3, so x = 1/2.


2. {{{(sqrt(49))^(1/2) = x}}}


{{{x = (+7)^(1/2)}}} or {{{x = (-7)^(1/2)}}}


{{{x = +sqrt(7)}}} or {{{x = -sqrt(7)}}} or {{{x = +sqrt(-7)}}} or {{{x = -sqrt(-7)}}}
{{{x = +sqrt(7)}}} or {{{x = -sqrt(7)}}} or {{{x = +sqrt(7*(-1))}}} or {{{x = -sqrt(7*(-1))}}}
{{{x = +sqrt(7)}}} or {{{x = -sqrt(7)}}} or {{{x = +sqrt(7)sqrt(-1)}}} or {{{x = -sqrt(7)sqrt(-1)}}}
{{{x = +sqrt(7)}}} or {{{x = -sqrt(7)}}} or {{{x = +sqrt(7)i}}} or {{{x = -sqrt(7)i}}}.


3. {{{1/16 = 16^x}}}
{{{16^(-1) = 16^x}}}


again, equating the 2 sides gives x = -1.


jon.