Expanding and Condensing Logarithms 2022

Front

What is the product rule of logarithms?

Back

The product rule states that log_b(mn) = log_b(m) + log_b(n), where b is the base.

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 b is the base.

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(m^k) = k * log_b(m), where b is the base.

Front

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

Back

6log_4(u) - 36log_4(v) is already in expanded form.

Front

Condense: log_8(x^3) + log_8(y^9)

Back

log_8(x^3y^9) using the product rule.

Front

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

Back

6log_8(u) - 2log_8(v) is already in expanded form.

Front

Expand: 4log_4(u) + 16log_4(v)

Back

4log_4(u) + 16log_4(v) is already in expanded form.

Front

Expand: log_7(x) + log_7(y) + 4log_7(z)

Back

log_7(xy) + log_7(z^4) using the product rule.

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.

Front

What is the change of base formula?

Back

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