Properties and Laws of Logarithms
Master the fundamental rules for expanding and condensing logarithmic expressions.
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Questions Covered in This Set
10 cards to master
What is the Product Rule for logarithms?
log_b(MN) = log_b(M) + log_b(N). The logarithm of a product equals the sum of the logarithms.
What is the Quotient Rule for logarithms?
log_b(M/N) = log_b(M) - log_b(N). The logarithm of a quotient equals the difference of logarithms.
What is the Power Rule for logarithms?
log_b(M^p) = p · log_b(M). The logarithm of a power equals the exponent times the logarithm.
What is the Change of Base Formula?
log_b(M) = log_a(M) / log_a(b). Used to convert logarithms to a different base, typically ln or log base 10.
What is log_b(b)?
log_b(b) = 1, because b^1 = b. This is the identity property of logarithms.
What is log_b(1)?
log_b(1) = 0, because b^0 = 1. This is the zero property of logarithms.
Expand: log_2(x^3 · y^2)
3log_2(x) + 2log_2(y). Apply the product rule, then the power rule to each term.
Condense: 4log(x) - 2log(y)
log(x^4/y^2). Apply the power rule first, then the quotient rule to combine.
What is the Inverse Property of logarithms?
log_b(b^x) = x and b^(log_b(x)) = x. Logarithms and exponents undo each other.
Why do the logarithm laws mirror exponent rules?
Because logarithms are exponents. The laws follow directly from properties of exponents like b^x · b^y = b^(x+y).
