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) About Me  (Show Source):
Answer by Edwin McCravy(20059) About Me  (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:


matrix%281%2C3%2C%0D%0Alog%28%2825%2A4%29%29-log%28%282%2A5%29%29%2C%22%22=%22%22%2C1%29

matrix%281%2C3%2C%0D%0Alog%28%2825%2A4%29%29-log%28%282%2A5%29%29%2C%22%22=%22%22%2C1%29%29

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

matrix%281%2C3%2C%0D%0Alog%28%28%2825%2A4%29%2F%282%2A5%29%29%29%2C%22%22=%22%22%2C1%29

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.



matrix%281%2C3%2C%0D%0Alog%28%285%2A2%29%29%2C%22%22=%22%22%2C1%29

matrix%281%2C3%2C%0D%0Alog%28%2810%29%29%2C%22%22=%22%22%2C1%29

The log of 10 in base 10 is 1.

matrix%281%2C3%2C%0D%0A1%2C%22%22=%22%22%2C1%29

Therefore it is proved.

Edwin