Expanding and Condensing 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, if b^y = x, then log_b(x) = y.

Front

What is the product rule of logarithms?

Back

The product rule states that log_b(MN) = log_b(M) + log_b(N), where M and N are positive numbers.

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that log_b(M/N) = log_b(M) - log_b(N), where M and N are positive numbers.

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(M^p) = p * log_b(M), where M is a positive number and p is any real number.

Front

Condense: 4log_3(x) - 4log_3(y)

Back

log_3(x^4/y^4)

Front

Expand: 6log_8(u) - 2log_8(v)

Back

log_8(u^6) - log_8(v^2)

Front

Condense: 15log_8(a/b^3)

Back

log_8(a^15/b^45)

Front

Expand: 6log_4(u) - 36log_4(v)

Back

log_4(u^6) - log_4(v^36)

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

What is the definition of a base in logarithms?

Back

The base in logarithms is the number that is raised to a power to obtain a certain value. In log_b(a), b is the base.