Expanding and Condensing Logarithms

Front

What is the product rule for 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 for 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 for 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

How do you condense the expression log_b(M) + log_b(N)?

Back

You can condense it to log_b(MN) using the product rule.

Front

How do you condense the expression log_b(M) - log_b(N)?

Back

You can condense it to log_b(M/N) using the quotient rule.

Front

How do you expand the expression p * log_b(M)?

Back

You can expand it to log_b(M^p) using the power rule.

Front

What is the definition of a logarithm?

Back

A logarithm log_b(a) is the exponent to which the base b must be raised to produce the number a.

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 relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other. If b^y = x, then log_b(x) = y.

Front

What is the value of log_b(b)?

Back

The value of log_b(b) is 1, since b^1 = b.