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

Convert log_2(32) = 5 to exponential form.

Back

2^5 = 32.

Front

Rewrite 3^4 = 81 in logarithmic form.

Back

log_3(81) = 4.

Front

What is the Power Property of logarithms?

Back

The Power Property states that log_b(a^c) = c * log_b(a).

Front

What is the Quotient Property of logarithms?

Back

The Quotient Property states that log_b(a/c) = log_b(a) - log_b(c).

Front

What is the Product Property of logarithms?

Back

The Product Property states that log_b(a * c) = log_b(a) + log_b(c).

Front

Simplify log_4(20) - 3log_4(x).

Back

log_4(20/x^3).

Front

Combine log_6(25) - log_6(5) into a single logarithm.

Back

log_6(5).

Front

Combine 2log(4) + log(2) into a single logarithm.

Back

log(32).

Front

What is the change of base formula for logarithms?

Back

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