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education/math/Logarithms.md
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@ -35,7 +35,7 @@ $$ log_5 y = 2 $$$$log_5(yz) = log_5 y + log_5 z $$$$ 2 + 3 = 5 $$
Exponents can be moved to the front of a logarithm Exponents can be moved to the front of a logarithm
$$ log_3 x^5 = 5*log_3 x $$ $$ log_3 x^5 = 5*log_3 x $$
Roots are just the inverse, so: Roots are just the inverse, so:
$$ log_3 sqrt(x) = \frac{1}{2}*log_3x $$ $$ log_3 \sqrt x = \frac{1}{2}*log_3x $$
## Change of base ## Change of base
$$ log_b x = \frac{\log x}{\log b} = \frac{\ln x}{\ln b} $$ $$ log_b x = \frac{\log x}{\log b} = \frac{\ln x}{\ln b} $$
The above are all equivalent because the ratios are the same The above are all equivalent because the ratios are the same