SOLUTION: the value of {{{log(7,(9))log(5,(7))log(3,(5))}}} is ?

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Question 322086: the value of log%287%2C%289%29%29log%285%2C%287%29%29log%283%2C%285%29%29 is ?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

log%287%2C%289%29%29log%285%2C%287%29%29log%283%2C%285%29%29

Use the change of base formula log%28%22OLD_BASE%22%2C%28X%29%29%22=%22log%28%22NEW_BASE%22%2C%28X%29%29%2Flog%28%22NEW_BASE%22%2C%28%22OLD_BASE%22%29%29 

for each of those logarithms:



Write 9 as 3%5E2






Use the rule of logarithms: log%28B%2C%28Y%5EX%29%29%22=%22X%2Alog%28B%2CY%29 to rewrite the leftmost numerator:



Everything cancels but the 2



Answer: 2

Edwin