Log Properties

Front

What is the property of logarithms that states Log_b(xy) = Log_b(x) + Log_b(y)?

Back

This property is known as the Product Property of Logarithms. It allows you to expand the logarithm of a product into the sum of the logarithms of the factors.

Front

Expand Log_3(5x) using the Product Property of Logarithms.

Back

Log_3(5x) = Log_3(5) + Log_3(x)

Front

What is the Quotient Property of Logarithms?

Back

The Quotient Property states that Log_b(x/y) = Log_b(x) - Log_b(y). It allows you to express the logarithm of a quotient as the difference of the logarithms.

Front

Use the Quotient Property to simplify Log_4(16/2).

Back

Log_4(16/2) = Log_4(16) - Log_4(2) = 2 - 0.5 = 1.5

Front

What is the Power Property of Logarithms?

Back

The Power Property states that Log_b(x^k) = k * Log_b(x). This property allows you to bring the exponent in front of the logarithm.

Front

Simplify Log_2(8^3) using the Power Property.

Back

Log_2(8^3) = 3 * Log_2(8) = 3 * 3 = 9.

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. This allows you to convert logarithms to a different base.

Front

Use the Change of Base Formula to calculate Log_10(100) using base 2.

Back

Log_10(100) = Log_2(100) / Log_2(10) = 6.643856 / 3.321928 = 2.

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

If Log_5(25) = x, what is the value of x?

Back

x = 2, because 5^2 = 25.