SOLUTION: I just can't get this! If a is a positive real number, such as a is not equal to 1, and a^x=b, then the logarthmic function is represented as what?

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Question 144391: I just can't get this!
If a is a positive real number, such as a is not equal to 1, and a^x=b, then the logarthmic function is represented as what?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a%5Ex=b Start with the given equation


log%2810%2C%28a%5Ex%29%29=log%2810%2C%28b%29%29 Take the log of both sides



x%2Alog%2810%2C%28a%29%29=log%2810%2C%28b%29%29 Rewrite the left side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


x=log%2810%2C%28b%29%29%2Flog%2810%2C%28a%29%29 Divide both sides by log%2810%2C%28a%29%29


x=log%28a%2C%28b%29%29 Simplify the right side by use of the change of base formula.