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 2^3, 2 is the base.

Front

How do you solve exponential equations with the same base?

Back

Set the exponents equal to each other and solve for the variable.

Front

What is the property of exponents when multiplying powers with the same base?

Back

Add the exponents: a^m * a^n = a^(m+n).

Front

What is the property of exponents when dividing powers with the same base?

Back

Subtract the exponents: a^m / a^n = a^(m-n).

Front

What is the value of 3^0?

Back

1, because any non-zero number raised to the power of zero is 1.

Front

Solve: 2^(x+3) = 32. What is x?

Back

x = 1, since 32 = 2^5.

Front

What is the first step in solving the equation 81^(3-x) = 3^(-5x+6)?

Back

Rewrite 81 as 3^4 to have the same base.

Front

If 3^(2x) = 27, what is x?

Back

x = 3/2, since 27 = 3^3.

Front

What does it mean to simplify an exponential expression?

Back

To rewrite it in a simpler form, often by combining like terms or reducing exponents.