Solving Exponential and Logarithmic Equations

Front

What is the change of base rule for logarithms?

Back

The change of base rule states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

What is the value of x in the equation log_2(x+3) = 4?

Back

x = 13.

Front

If log_5(4x-7) = log_5(x+5), what is the value of x?

Back

x = 4.

Front

Solve for x: 3^(2x - 6) = 81.

Back

x = 5.

Front

What is the solution to the equation log(x) + log(x+3) = 1?

Back

x = 2.

Front

Define an exponential equation.

Back

An exponential equation is an equation in which a variable appears in an exponent.

Front

What is the general form of a logarithmic function?

Back

The general form is y = log_b(x), where b is the base.

Front

What does it mean for a logarithm to be undefined?

Back

A logarithm is undefined for non-positive arguments (x ≤ 0).

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions are the inverse of logarithmic functions.

Front

How do you solve an exponential equation?

Back

To solve an exponential equation, you can take the logarithm of both sides.