Expanding and Condensing Logarithms

Front

What is the product rule of logarithms?

Back

log_b(MN) = log_b(M) + log_b(N) - This rule states that the logarithm of a product is the sum of the logarithms of the factors.

Front

What is the quotient rule of logarithms?

Back

log_b(M/N) = log_b(M) - log_b(N) - This rule states that the logarithm of a quotient is the difference of the logarithms.

Front

What is the power rule of logarithms?

Back

log_b(M^k) = k * log_b(M) - This rule states that the logarithm of a number raised to a power is the power times the logarithm of the number.

Front

Condense the expression: log_a(x) + log_a(y) + log_a(z^3)

Back

log_a(xyz^3) - This uses the product rule of logarithms.

Front

Expand the expression: log_8(u^6) - log_8(v^2)

Back

6log_8(u) - 2log_8(v) - This uses the power and quotient rules of logarithms.

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, log_b(a) = c means b^c = a.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) - This formula allows you to change the base of a logarithm.

Front

Condense the expression: 3log_5(x) + 2log_5(y)

Back

log_5(x^3y^2) - This uses the power and product rules of logarithms.

Front

Expand the expression: log_2(8)

Back

log_2(2^3) = 3log_2(2) = 3 - This uses the power rule of logarithms.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.