Properties of Logarithms

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. For example, log_b(a) = c means b^c = a.

Front

What is the product property of logarithms?

Back

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

Front

What is the quotient property of logarithms?

Back

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

Front

What is the power property of logarithms?

Back

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

Front

True or False: log 10 - log 5 = log 2.

Back

False.

Front

Expand log_6(5x^3/y).

Back

log_6(5) + 3*log_6(x) - log_6(y).

Front

Write log_b(xy) as two logs.

Back

log_b(x) + log_b(y).

Front

Write log_b(x/y) as two logs.

Back

log_b(x) - log_b(y).

Front

If log_b(2) = 0.301 and log_b(3) = 0.477, what is log_b(6)?

Back

log_b(6) = log_b(2*3) = log_b(2) + log_b(3) = 0.301 + 0.477 = 0.778.

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.