2. a) [tex] log_{11}(14641)=4 [/tex]
b) [tex] log_{4}(200)- log_{3}(50)= log_{ 2^{2} }(200)- log_{3}(50)= \frac{1}{2}* log_{ 2 }(200)- log_{3}(50) [/tex]
c) [tex] log_{5}(140)- log_{5}(7)- log_{5}(10)+ log_{5}(50)= [/tex][tex] log_{5}(140)+ log_{5}(50)- log_{5}(7)- log_{5}(10)= [/tex][tex]log_{5}(140)+ log_{5}(50)- (log_{5}(7)+ log_{5}(10))=log_{5}( \frac{140*50}{7*10} ) [/tex][tex]log_{5}(20*5 )=log_{5}(100 )=log_{5}(10 ^{2} )=2log_{5}(10 )=2log_{5}(5*2 )=[/tex]
[tex]2(log_{5}(5)+ log_{5}( 2) )=2(1+log_{5}( 2) ) =2+2log_{5}( 2) [/tex]
