Solving Exponential Equations

Front

What is an exponential equation?

Back

An equation in which a variable appears in the exponent, such as a^x = b.

Front

What is the base in an exponential expression?

Back

The number that is raised to a power, for example, in 2^x, 2 is the base.

Front

How do you solve the equation 2^x = 8?

Back

Convert 8 to a power of 2: 2^x = 2^3, so x = 3.

Front

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

Back

This is known as the Product of Powers Property.

Front

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

Back

This is known as the Power of a Power Property.

Front

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

Back

Rewrite both sides with the same base: 16 = 2^4 and 64 = 2^6, then solve for x.

Front

What is the solution to the equation 2^x = 4^(x+1)?

Back

Rewrite 4 as 2^2: 2^x = (2^2)^(x+1) = 2^(2x+2), so x = -2.

Front

How do you solve the equation 5^(-3x - 1) = 25?

Back

Rewrite 25 as 5^2: 5^(-3x - 1) = 5^2, so -3x - 1 = 2, leading to x = -1.

Front

What is the solution to the equation 3^3 = 3^(4x + 2)?

Back

Since the bases are the same, set the exponents equal: 3 = 4x + 2, leading to x = 1/4.

Front

What is the Exponential Growth Formula?

Back

The formula is A = P(1 + r)^t, where A is the amount, P is the principal, r is the rate, and t is time.