Solving Exponential Equations with the Same Bases

Front

What is an exponential equation?

Back

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

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 base in an exponential expression?

Back

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

Front

What is the first step to solve 4^(p+2) = 64?

Back

Rewrite 64 as a power of 4, since 64 = 4^3.

Front

If 5^(a + 2) = 1/125, how can you express 1/125?

Back

Rewrite 1/125 as 5^(-3) because 125 = 5^3.

Front

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

Back

x = -1, since 25 = 5^2.

Front

How do you rewrite 8 as a power of 2?

Back

8 can be rewritten as 2^3.

Front

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

Back

x = -2, since 4 = 2^2.

Front

What does it mean to have the same base in exponential equations?

Back

It means both sides of the equation can be expressed with the same base, allowing for easier comparison of exponents.

Front

What is the property of exponents used when multiplying like bases?

Back

a^m * a^n = a^(m+n).