SOLUTION: log9^3

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Question 251388: log9^3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 we can rewrite log%2810%2C%289%5E3%29%29 as 3%2Alog%2810%2C%289%29%29. So log%2810%2C%289%5E3%29%29=3%2Alog%2810%2C%289%29%29

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Edit: If the log looks like this: log%289%2C%283%29%29, then disregard the last portion


Let y=log%289%2C%283%29%29. Using the property log%28b%2C%28x%29%29=y <=> b%5Ey=x, we can rewrite y=log%289%2C%283%29%29 as 9%5Ey=3.

Now rewrite 9 as 3%5E2 and 3 as 3%5E1 to get %283%5E2%29%5Ey=3%5E1 and multiply the exponents to get 3%5E%282y%29=3%5E1


Since the bases are equal, the exponents are equal. So 2y=1 giving us the solution of y=1%2F2


Since y=log%289%2C%283%29%29, this means log%289%2C%283%29%29=1%2F2 which is our answer.