Question 1002181
a).

{{{2^(2/log(5,x)) =1/16 }}}

{{{2^(2/log(5,x)) =1/2^4 }}}

{{{2^(2/log(5,x)) =2^(-4 )}}}.........if bases same, exponents are same to

{{{2/log(5,x) = -4 }}}

{{{2= -4log(5,x)}}} 

{{{2/-4= log(5,x)}}} 

{{{-1/2= log(5,x)}}} ......change the base to base {{{10}}}

{{{-1/2= log(x) /log(5)}}}

{{{-(1/2)log(5)= log(x) }}}

{{{log(5^(-1/2))= log(x) }}}

{{{log(1/5^(1/2))= log(x) }}}

{{{log(1/sqrt(5))= log(x)}}} .....if log same, then

{{{x=1/sqrt(5)}}}



b.) 

{{{log(4,(x+2))=log(4, x)+log(4, 2)}}}

{{{log(4,(x+2))=log(4, 2x)}}}...if base same and log same, we have

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

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

{{{x=2}}}



c.)

{{{5^(2^x)=3}}}....take the log of both sides

{{{log(5^(2^x))=log(3)}}}

{{{(2^x)log(5)=log(3)}}}

{{{2^x=log(3)/log(5)}}}....take the log of both sides again

{{{log(2^x)=log((log(3)/log(5)))}}}

{{{xlog(2)=log((log(3)))-log((log(5)))}}}

{{{xlog(2)=log((log(3)))-log((log(5)))}}}

{{{x=(log((log(3)))-log((log(5))))/log(2)}}}