3.4 - Solving Logarithmic Equations

Front

What is the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately equal to 2.71828.

Front

What is the property of logarithms that states log(a) + log(b) = log(ab)?

Back

This property is known as the Product Rule of Logarithms.

Front

What is the property of logarithms that states log(a) - log(b) = log(a/b)?

Back

This property is known as the Quotient Rule of Logarithms.

Front

What is the property of logarithms that states k * log(a) = log(a^k)?

Back

This property is known as the Power Rule of Logarithms.

Front

Solve: log(x) + log(x+3) = 1

Back

x = 2

Front

Solve: log_5(4x - 7) = log_5(x + 5)

Back

x = 4

Front

Solve: log_2(x + 4) - log_2(7) = 2

Back

x = 24

Front

Solve: -6log_3(x - 3) = -24

Back

x = 84

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

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.