Logarithm (Base a)
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| Logarithm (Base a)
The logarithm of [math]x\,[/math] to the base [math]a\,[/math], denoted by [math]log_{a}x\,[/math], is that real number [math]u\,[/math] such that [math]a^u=x\,[/math] , where [math]x\gt0\,[/math] and [math]a\,[/math] is a positive constant other than [math]1\,[/math].
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Examples
- [math]10\,000=10^4\,[/math]. The exponent to which we raise [math]10\,[/math] to get [math]10\,000\,[/math] is [math]4\,[/math], so [math]\log_{10}10\,000=4\,[/math]
- [math]8=2^3\,[/math]. The exponent to which we raise [math]2\,[/math] to get [math]8\,[/math] is [math]3\,[/math], so [math]\log_{2}8=3\,[/math]
- [math]1=6^0\,[/math]. The exponent to which we raise [math]6\,[/math] to get [math]1\,[/math] is [math]0\,[/math], so [math]\log_{6}1=0.\,[/math]
- [math]3=\sqrt{9}=9^{\tfrac {1}{2}}[/math]. The exponent to which we raise [math]9\,[/math] to get [math]3\,[/math] is [math]\tfrac {1}{2}\,[/math], so [math]\log_{9}3=\tfrac {1}{2}\,[/math]
- [math]8=8^1\,[/math]. The exponent to which we raise [math]8\,[/math] to get [math]8\,[/math] is [math]1\,[/math], so [math]\log_{8}8=1\,[/math]
