7.4 Expanding/Condensing Logs

Front

What is the product rule of logarithms?

Back

log_b(mn) = log_b(m) + log_b(n) for any positive numbers m and n.

Front

What is the quotient rule of logarithms?

Back

log_b(m/n) = log_b(m) - log_b(n) for any positive numbers m and n.

Front

What is the power rule of logarithms?

Back

log_b(m^p) = p * log_b(m) for any positive number m and any real number p.

Front

Convert log_2(8) to exponential form.

Back

2^3 = 8.

Front

Convert log_5(25) to exponential form.

Back

5^2 = 25.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

Rewrite log_10(1000) in terms of powers of 10.

Back

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

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

If log_b(x) = y, what is the equivalent exponential form?

Back

b^y = x.

Front

What is the value of log_10(1)?

Back

0, because 10^0 = 1.