Exponential Equations (same base)

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

How do you solve exponential equations with the same base?

Back

To solve exponential equations with the same base, set the exponents equal to each other and solve for the variable. For example, if 3^(2x) = 3^(x-7), then 2x = x - 7.

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. In 5^a, 5 is the base.

Front

What is the exponent in an exponential expression?

Back

The exponent indicates how many times the base is multiplied by itself. In 2^3, 3 is the exponent, meaning 2 is multiplied by itself three times (2 * 2 * 2).

Front

If 27^(2x) = 3^(x-7), what is the first step to solve for x?

Back

Rewrite both sides with the same base. Since 27 = 3^3, rewrite the left side as (3^3)^(2x) = 3^(x-7).

Front

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

Back

The solution is a = -5, since 1/125 can be rewritten as 5^(-3), leading to a + 2 = -3.

Front

How do you express 256 as a power of 16?

Back

256 can be expressed as 16^(2), since 16^2 = 256.

Front

What is the solution to the equation 12^(2x-10) = 1?

Back

The solution is x = 5, since 12^(2x-10) = 1 implies 2x - 10 = 0.

Front

What does it mean if two exponential expressions are equal?

Back

If two exponential expressions are equal, their bases must be the same, and their exponents must also be equal.

Front

How can you check your solution for an exponential equation?

Back

You can check your solution by substituting the value back into the original equation to see if both sides are equal.