SOLUTION: Which of the following cannot be a base for exponential and logarithmic functions? 0.1 π 1 e

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Question 148216: Which of the following cannot be a base for exponential and logarithmic functions?
0.1
π
1
e
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1 cannot be a base because raised to any power, it's still 1.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The previous solution is correct, but there's more to this solution. Let's say that you could have a base of 1. So this means that 1%5Ex=y can be written as log%281%2C%28y%29%29=x by use of the property b%5Ey=x ===> log%28b%2C%28x%29%29=y


Now using the change of base formula, we can rewrite log%281%2C%28y%29%29=x as log%2810%2C%28y%29%29%2Flog%2810%2C%281%29%29=x. However, log%2810%2C%281%29%29=0 which means that log%2810%2C%28y%29%29%2Flog%2810%2C%281%29%29=x becomes log%2810%2C%28y%29%29%2F0=x. Since you cannot divide by zero, this means that a base of 1 is not possible for a logarithmic function.