Expand and Condense Logs Practice

Front

What does it mean to condense logarithmic expressions?

Back

Condensing logarithmic expressions involves combining multiple logarithms into a single logarithm using the properties of logarithms, such as the product, quotient, and power rules.

Front

What is the logarithmic form of the equation 3^4 = 81?

Back

The logarithmic form is log_3(81) = 4.

Front

What is the value of log_9(9)?

Back

The value of log_9(9) is 1, because any logarithm of a number to its own base is 1.

Front

What does it mean to expand logarithmic expressions?

Back

Expanding logarithmic expressions involves breaking down a single logarithm into multiple logarithms using the properties of logarithms.

Front

What is the value of log_b(b)?

Back

The value of log_b(b) is 1, as any logarithm of a number to its own base is 1.

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

How do you convert a logarithmic equation to an exponential equation?

Back

To convert log_b(a) = c to exponential form, use the definition of logarithms: b^c = 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.