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education/math/Logarithms.md
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@ -13,12 +13,12 @@ $$ \sqrt{x} = x^{1/2} $$
To get the reciprocal of a value, change the sign of the exponent. To get the reciprocal of a value, change the sign of the exponent.
$$ x^{-1} = \frac{1}{x} $$ $$ x^{-1} = \frac{1}{x} $$
## Domain ## Domain
There are 3 places you need to worry about domain. There are 3 places you need to worry about domain. The third is specific to logarithms.
- You can't divide by 0 - You can't divide by 0
- You can't take the square root of a negative without complex numbers - You can't take the square root of a negative without complex numbers
- You cannot take the $log$ of a zero, or a negative number. - You cannot take the $log$ of a zero, or a negative number.
- There's no way to raise a number to an exponent and have it equal zero, or be a negative number. - There's no way to raise a number to an exponent and have it equal zero, or be a negative number.
- This can be used to help solve inequalities, because you know an equation that's wrapped in a logarithm must be $> 0$. - This can be used to help solve inequalities, because you know *an equation that's wrapped in a logarithm must be $> 0$*.
### Finding the domain of added logarithms ### Finding the domain of added logarithms
$$ log(x+2) + log(2x-3) $$ $$ log(x+2) + log(2x-3) $$