Solving Exponential Equations

An exponential equation is an equation in which a variable appears in the exponent. For example, in the equation 2^x = 8, x is the variable in the exponent.

To solve, rewrite 1/125 as 5^(-3). Thus, a + 2 = -3, leading to a = -5.

Convert 8 to a power of 2: 8 = 2^3. Then set the exponents equal: 3 = 5x + 7.

Rewrite 512 as a power of 2: 512 = 2^9. Set the exponents equal: x + 1 = 9, leading to x = 8.

Rewrite 1/16 as 4^(-2). Thus, 3b - 3 = -2, leading to b = 1/3.

The base is the constant that is raised to a power. In the function f(x) = a^x, 'a' is the base.

This is known as the Product of Powers Property.

This is known as the Power of a Power Property.

This is known as the Quotient of Powers Property.

1/125 can be expressed as 5^(-3).