Logarithm Properties

Front

What is the product property of logarithms?

Back

log_b(mn) = log_b(m) + log_b(n) for any positive numbers m and n.

Front

What is the quotient property of logarithms?

Back

log_b(m/n) = log_b(m) - log_b(n) for any positive numbers m and n.

Front

What is the power property of logarithms?

Back

log_b(m^p) = p * log_b(m) for any positive number m and real number p.

Front

Expand: log_8(xy)

Back

log_8(x) + log_8(y) using the product property.

Front

Expand: log_8(x^5)

Back

5 * log_8(x) using the power property.

Front

Condense: log_8(x) + log_8(y) + log_8(z)

Back

log_8(xyz) using the product property.

Front

Condense: 3 * log_8(x) - log_8(y)

Back

log_8(x^3/y) using the quotient and power properties.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any positive number k.

Front

If log_b(x) = p, what is x in terms of b and p?

Back

x = b^p.

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.