vault backup: 2024-01-29 10:22:52
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@ -35,7 +35,7 @@ $$ log_5 y = 2 $$$$log_5(yz) = log_5 y + log_5 z $$$$ 2 + 3 = 5 $$
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Exponents can be moved to the front of a logarithm
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$$ log_3 x^5 = 5*log_3 x $$
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Roots are just the inverse, so:
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$$ log_3 sqrt(x) = \frac{1}{2}*log_3x $$
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$$ log_3 \sqrt x = \frac{1}{2}*log_3x $$
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## Change of base
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$$ log_b x = \frac{\log x}{\log b} = \frac{\ln x}{\ln b} $$
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The above are all equivalent because the ratios are the same
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