Properties of Logs Practice

Front

What is the product property of logarithms?

Back

The product property states that log_b(mn) = log_b(m) + log_b(n), where b is the base, and m and n are positive numbers.

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(m/n) = log_b(m) - log_b(n), where b is the base, and m and n are positive numbers.

Front

What is the power property of logarithms?

Back

The power property states that log_b(m^k) = k * log_b(m), where b is the base, m is a positive number, and k is any real number.

Front

Condense: log(4) + log(x)

Back

log(4x) using the product property.

Front

Condense: log(16) + log(2) - log(8)

Back

log(4) using the product and quotient properties.

Front

Expand: log(3x^2)

Back

2log(3) + log(x) using the power property.

Front

Expand: log(5xy)

Back

log(5) + log(x) + log(y) using the product property.

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.

Front

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

Back

b^y = x.

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.