Question 1087750

a) 

{{{9log(5 , x) =log (5,x)}}}

 {{{log(5 , x^9) =log (5,x)}}} since log and base same

{{{x^9 =x}}}
{{{x^cross(9)^8 =cross(x)1}}}
{{{x^8 =1}}}

=>{{{x=1}}}

B)

 {{{log (8,x/2 ) = log (2,x )}}} ...in base {{{10}}} will be 

{{{ log (x/2 ) / log (8 )= log (x ) / log (2)}}}

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

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

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

 {{{log (x/2 ) =3cross(log (2))( log (x ) / cross(log (2)))}}}

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

{{{ log (x/2 ) = log (x^3 ) }}} if so, than

{{{x/2  = x^3 }}}

{{{x = 2x^3 }}}

{{{cross(x)1 = 2x^cross(3)^2 }}}

{{{1 = 2x^2 }}}

{{{x^2=1/2}}}

{{{x = 1/sqrt(2)}}}