document.write( "Question 148216: Which of the following cannot be a base for exponential and logarithmic functions?
\n" ); document.write( " 0.1
\n" ); document.write( " π
\n" ); document.write( " 1
\n" ); document.write( " e
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Algebra.Com's Answer #108621 by jim_thompson5910(35256) $\"\"$ $\"About$

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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 $\"b%5Ey=x\"$ ===> $\"log%28b%2C%28x%29%29=y\"$ \r
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\n" ); document.write( "\n" ); document.write( "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. \n" ); document.write( "

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