Question 1153167


(1) 

{{{log(3, 1/9)}}}
={{{log(3, 1)-log(3,9)}}}
={{{0-2}}}
={{{-2}}}

(2) 

{{{log(3^3) +log(3^9)}}}

={{{3log(3) +9log(3)}}}

={{{12log(3)}}}


(3) 

{{{log(6, 216)=3}}}

={{{log( 216)/log(6)=3}}}

={{{log( 216)=3log(6)}}}

={{{log( 216)=log(6^3)}}}

={{{216=6^3}}}

={{{216=216}}}-> true


(4) 

{{{log(8 ,4) + log(8 ,16)}}}

={{{log(4)/log(8) + log(16)/log(8)}}}

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

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

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

={{{(cross(6)2 cross(log(2)))/cross(3)cross(log(2))}}}

={{{2}}}

(5) 

{{{log(12, 288)- log(12, 2)}}}

={{{log(288)/log(12)- log(2)/log(12)}}}

={{{(log(288)- log(2))/log(12)}}}........{{{log(288)=log(2^5*3^3)=5log(2) + 2 log(3)}}} and {{{log(12)=log(2^2*3)=2log(2) +  log(3)}}}

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

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

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

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

={{{2}}}


(6). 

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

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

={{{log(10)}}}

={{{1}}}


(7) 

{{{log(10,10)=1}}}
{{{log(10)/log(10)=1}}}
{{{1=1}}}

(8) 

{{{3^7=2187}}}

{{{3*3*3*3*3*3*3=2187}}}

{{{2187=2187}}}

(9) 

{{{4^p=q}}}

{{{log(4^p)=log(q)}}}

{{{p*log(4)=log(q)}}}

{{{p=log(q)/log(2^2)}}}

{{{p=log(q)/2log(2)}}}

(10) 

{{{x^y=2}}}

{{{log(x^y)=log(2)}}}

{{{y*log(x)=log(2)}}}

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