12.6 - Exponential equations

Before reading this section you may find it helpful to review the following topics:

Basic procedures for solving equations.
Exponents.
Logarithms.

An exponential equation is one in which the variable to be solved for (call it x) is in an exponent. For example 3^x = 5 is an exponential equation while 3⁵ = x is not.

Only certain types of exponential equations can be solved using algebra. We will study the following types:

• The unknown, x, occurs only once. Example Go to topic

• The equation is of the form a · b^x = c · d^x. Example Go to topic

• The only exponential in the equation is b^x, and it occurs several times. Example Go to topic

• The equation contains the exponentials b^x, b^2 x, b^3 x, etc. Example Go to topic

• The unknown, x, occurs only once.	Example	Go to topic
• The equation is of the form a · b^x = c · d^x.	Example	Go to topic
• The only exponential in the equation is b^x, and it occurs several times.	Example	Go to topic
• The equation contains the exponentials b^x, b^2 x, b^3 x, etc.	Example	Go to topic