Problem#2 Show that 1/log_6(24)+1/log_12(24)+1/log_824=2

Source: Yahoo Answers. The question and my answer here.

Show that 1/log_6(24)+1/log_12(24)+1/log_824=2

My answer:

Remember:
1/log_A(B)=1/(log_m(B)/log_m(A)
=log_m(A)/log_m(B)

To show that 1/log_6(24)+1/log_12(24)+1/log_824=2
LHS :
1/log_6(24)+1/log_12(24)+1/log_824
=log6/log24+log12/log24+log8/log24
=(log6+log12+log8)/log24

Now remember logA+logB=log(AxB)
Hence
=log(6x12x8)/log24
=log576/log24
=log24^2/log24
=2log24/log24
=2 :)

Source: http://tinyurl.com/6box2u5