Solving Exponential Equations

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 variable in the exponent.

Front

How do you solve an exponential equation with the same base?

Back

To solve an exponential equation with the same base, set the exponents equal to each other. For example, if 3^x = 3^4, then x = 4.

Front

What is the first step in solving the equation 9^(8-x) = 27^(x-3)?

Back

The first step is to express both sides of the equation with the same base. Here, 9 can be written as 3^2 and 27 as 3^3.

Front

Solve: 9^(8-x) = 27^(x-3)

Back

x = 5

Front

What is the relationship between exponents and logarithms?

Back

Logarithms are the inverse operations of exponentiation. For example, if a^b = c, then log_a(c) = b.

Front

How do you solve the equation 7^(-x) = 49?

Back

Rewrite 49 as 7^2, then set the exponents equal: -x = 2, leading to x = -2.

Front

Solve: 7^(-x) = 49

Back

x = -2

Front

What is the base of an exponential function?

Back

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

Front

How do you solve for x in the equation 16^(x+5) = 64^(-2)?

Back

Rewrite both sides with the same base: 16 = 2^4 and 64 = 2^6, then set the exponents equal.

Front

Solve: 16^(x+5) = 64^(-2)

Back

x = -8