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education/math/Logarithms.md
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@ -22,4 +22,15 @@ There are 3 places you need to worry about domain.
## Adding logarithms ## Adding logarithms
$$ log(x+2) + log(2x-3) $$ $$ log(x+2) + log(2x-3) $$
With the above example, you can find the domain of each function separately, then find the overlap of valid numbers. With the above example, you can find the domain of each function separately, then find the overlap of valid numbers.
# Expanding logarithms
$$ log_b(x*y) = log_b x + log_b y $$
$$log_b(\frac{x}{y}) = log_b x - log_b y $$
Example Problem:
$$ log_5 z = 3 $$
$$ log_5 y = 2 $$$$log_5(yz) = log_5 y + log_5 z $$$$ 2 + 3 = 5 $$
Exponents can be moved to the front of a logarithm
$$ log_3 x^5 = 5*log_3 x $$