Properties of Logs

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, where k is the new base.

Front

What does it mean to expand a logarithm?

Back

Expanding a logarithm involves breaking it down into simpler components using logarithmic properties, such as the product, quotient, and power rules.

Front

What is the product rule of logarithms?

Back

The product rule states that log_b(xy) = log_b(x) + log_b(y).

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(x^k) = k * log_b(x).

Front

How do you condense logarithmic expressions?

Back

Condensing logarithmic expressions involves combining multiple logs into a single log using the product, quotient, and power rules.

Front

What is the value of log_10(1000)?

Back

log_10(1000) = 3, because 10^3 = 1000.

Front

What is log_b(1)?

Back

log_b(1) = 0 for any base b > 0, because b^0 = 1.

Front

What is log_b(b)?

Back

log_b(b) = 1 for any base b > 0, because b^1 = b.

Front

How do you evaluate log_2(8)?

Back

log_2(8) = 3, because 2^3 = 8.