SOLUTION: Show that log25+log4-log2-log5=1

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Question 1073878: Show that log25+log4-log2-log5=1
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!






True.

Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!


Group the first two and the last two (taking out a -
in the last two changes the - signs inside the parentheses
to + :



Use the principle that the SUM of two logs of numbers is 
the log of their PRODUCT:






Use the principle that the DIFFERENCE of two logs of numbers is 
the log of their QUOTIENT: 



The 2 on the bottom cancels into the 4 on the top and gives 2 on top.
The 5 on the bottom cancels into the 25 on the top and gives 5 on top.







The log of 10 in base 10 is 1.



Therefore it is proved.

Edwin
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