Lesson

An **exponential expression** is an expression of the form A^x where A is a positive number and x is a pronumeral. A is called the **base** of the exponential. An **exponential equation** is an equation where one or both sides are exponential expressions. To solve an exponential equation, we can write both sides of the equation as exponentials with the same base and then the indices will be equal.

Solve 4^{x}=4^{8}.

Worked Solution

Solve 8^{x}=\dfrac{1}{8^2}.

Worked Solution

Solve 25^{x+1}=125^{3x-4}.

Worked Solution

Idea summary

An **exponential expression** is an expression of the form A^x where A is a positive number and x is a pronumeral.

A is called the **base** of the exponential.

An **exponential equation** is an equation where one or both sides are exponential expressions.

To solve an exponential equation, we can write both sides of the equation as exponentials with the same base and then the indices will be equal.

Explore the connection between algebraic and graphical representations of relations such as simple quadratic, reciprocal, circle and exponential, using digital technology as appropriate