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 the equation 4^(p+2) = 64?

Back

To solve 4^(p+2) = 64, rewrite 64 as 4^3. Thus, p+2 = 3, leading to p = 1.

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 express 25 as a power of 5?

Back

25 can be expressed as 5^2.

Front

What is the solution to the equation 5^(-3x - 1) = 25?

Back

The solution is x = -1.

Front

How do you solve the equation 9^(8-x) = 27^(x-3)?

Back

Rewrite 9 as 3^2 and 27 as 3^3. The equation becomes (3^2)^(8-x) = (3^3)^(x-3). Simplifying gives 2(8-x) = 3(x-3), leading to x = 5.

Front

What is the property of exponents that states a^m * a^n = a^(m+n)?

Back

This property is known as the Product of Powers Property.

Front

How do you solve the equation 3^(2x+4) = 27^(2x-4)?

Back

Rewrite 27 as 3^3. The equation becomes 3^(2x+4) = (3^3)^(2x-4). Simplifying gives 2x + 4 = 3(2x - 4), leading to x = 4.

Front

What is the solution to the equation 2^(-m) = 2^(3m-3)?

Back

The solution is m = 3/4.

Front

What is the Exponential Growth Formula?

Back

The Exponential Growth Formula is A = Pe^(rt), where A is the amount of money accumulated after time t, P is the principal amount, r is the rate of interest, and t is the time.