25 lines
1.0 KiB
Markdown
25 lines
1.0 KiB
Markdown
https://www.youtube.com/watch?v=sULa9Lc4pck
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$$log_a(b) $$
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Pronounced log *base* a, this function is used to figure out what exponent you need to raise $a$ to to get $b$.
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$log_ab = c$ can be rewritten as $a^c = b$.
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$$ 5^{log_5^{(x+2)}}=x+2 $$
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By default, $log$ refers to $log_{10}$. $ln$ is shorthand for $log_e$.
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$$ \sqrt{x} = x^{1/2} $$
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To get the reciprocal of a value, change the sign of the exponent.
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$$ x^{-1} = \frac{1}{x} $$
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## Domain
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There are 3 places you need to worry about domain.
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- You can't divide by 0
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- You can't take the square root of a negative without complex numbers
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- You cannot take the $log$ of a zero, or a negative number.
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- There's no way to raise a number to an exponent and have it equal zero, or be a negative number.
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- This can be used to help solve inequalities, because you know an equation that's wrapped in a logarithm must be $> 0$.
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## Adding logarithms
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$$ log(x+2) + log(2x-3) $$
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With the above example, you can find the domain of each function separately, then find the overlap of valid numbers. |