Question 1153153
A) 

{{{log(5, 27)*log(2, 25)+log(3, 16)}}}

={{{(log( 27)/log(5))*(log(25)/log(2))+log( 16)/log(3)}}}

={{{(log( 3^3)/log(5))*(log(5^2)/log(2))+log( 2^4)/log(3)}}}

={{{(3log( 3)/log(5))*(2log(5)/log(2))+4log( 2)/log(3)}}}

={{{6log( 3)/log(2)+4log(2)/log(3)}}}

={{{(6log(3)*log(3))/(log(3)*log(2))+(4log(2)log(2))/(log(3)*log(2))}}}

={{{(6log^2(3)+4log^2( 2))/(log(3)log(2))}}}

={{{12.035}}}


(B) 

{{{log(m, m^3) + log( k,4) - log(p, p)}}}...............{{{log(p, p)=1}}}

{{{log(m^3)/log(m) + log( 2^2)/log( k) -1}}}

{{{3log(m)/log(m) + 2log( 2)/log( k) -1}}}

{{{3cross(log(m))/cross(log(m)) + 2log( 2)/log( k) -1}}}

{{{3 + 2log( 2)/log( k) -1}}}

{{{2 + 2log( 2)/log( k) }}}


(C) 

{{{log(500) - log(5)- log(10^3)}}}

{{{log(5*100) - log(5)- 3log(10)}}}

{{{log(5*10^2) - log(5)- 3log(10)}}}

{{{log(5)+log(10^2) - log(5)- 3(log(10))}}}

{{{cross(log(5))+2log(10) - cross(log(5))- 3(log(10))}}}

{{{2log(10) - 3(log(10))}}}

 {{{- (log(10))}}}

{{{- (log(2*5))}}}

{{{- (log(2)+log(5))}}}