Log Rules (without exponents)

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to memorize log rules

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Last updated 8:08 PM on 6/25/26

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1

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Log Definition

If y = b^x, then log_b(y) = x.

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Change of Base Formula

log_b(r) = log(r) / log(b)

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Product Rule of Logarithms

log_b(x ∙ y) = log_b(x) + log_b(y)

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Quotient Rule of Logarithms

log_b(x/y) = log_b(x) - log_b(y)

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Power Rule of Logarithms

log_b(rⁿ) = n log_b(r)

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What does “m” represent in: h = m^w ←→ log_m(h) = w.

base

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What does “p” represent in: log_f(g) = p.

exponent