Find the exact value of the logarithmic expession

[Math Tutor]

[tex]log_{12}18*log_{24}54 + 5(log_{12}18 - log_{24}54) = ?[/tex]

[Guest]

1? tell me if its correct and i am going to write the whole solution tomorrow ;]

[Math Tutor]

Yes, It is correct!

[Guest]

[tex]\frac {log_{3} 18}{ log_{3} 12 }[/tex]

[Guest]

i meant to take a preview with the last post sry clicked submit by accident
...
we need to change the base to 3 after that we need to use [tex]log_{a}{bc}=log_{a}b +log_{a}c[/tex]

than the expression will have ingegers only and [tex]log_{3}2[/tex]
for the sake of simplicity lets say that [tex]log_{3}2=b[/tex]

after simplifying the expression we get [tex]\frac {6b^2+5b+1}{6b^2+5b+1}=1[/tex]

[Guest]

The question is: how do you figure out that the answer is 1 without doing any additional calculations? YS

[Guest]

By the way I also does not understand your calculations.

[Guest]

just change the base to 3 and use this [tex]log_{a}{bc}=log_{a}b +log_{a}c[/tex] and you will understand everything....