Question 1205851: Express as logarithms of single number 2-2log 5 base 3
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your expression is 2 minus 2 * log3(5).
2 is equivalent to log3(9).
your expression becomes log3(9) - log3(25)
this becomes log3(9/25)
log3(9/25) is equal to log(9/25)/log(3) = -.9299470414
2 - 2 * log3(5) is equivalent to 2 - 2 * log(5)/log(3) which is equal to -.9299470414.
they give you the same answer, so 2 - 2 * log3(5) is equivalent to log3(9/25).
a couple of basic properties of logs are active here.
these are the properties as they apply to this problem.
log3(x) = log(x) / log(3)
log3(x) = y if and only if 3^y = x
your solution is that 2 - 2 * log3(5) is equivalent to log3(9/25).
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