14.2 Solving Exponential Equations with Common Bases

Front

What is an exponential equation?

Back

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 exponent.

Front

What is the base in an exponential expression?

Back

The base is the number that is raised to a power in an exponential expression. For example, in 5^a, 5 is the base.

Front

How do you solve exponential equations with common bases?

Back

To solve exponential equations with common bases, rewrite both sides of the equation with the same base and then set the exponents equal to each other.

Front

What is the solution to the equation 5^(a + 2) = 1/125?

Back

a = -5.

Front

What is the solution to the equation 7^(-x) = 49?

Back

x = -2.

Front

How do you express 1/125 as a power of 5?

Back

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

Front

What is the value of x in the equation 2^x = 4^(x + 1)?

Back

x = -2.

Front

What is the solution to the equation 3^3 = (3^2)^(2x + 1)?

Back

x = 1/4.

Front

What does it mean to have equal bases in exponential equations?

Back

Having equal bases means that both sides of the equation can be expressed with the same base, allowing for the exponents to be set equal to each other.

Front

What is the first step in solving the equation 5^(a + 2) = 1/125?

Back

Rewrite 1/125 as a power of 5, which is 5^(-3).