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 exponential equations with the same base?

Back

To solve exponential equations with the same base, set the exponents equal to each other. For example, if 3^x = 3^4, then x = 4.

Front

What is the first step in solving the equation 9^(8-x) = 27^(x-3)?

Back

The first step is to express both sides of the equation with the same base. Here, 9 can be written as 3^2 and 27 as 3^3.

Front

Solve: 9^(8-x) = 27^(x-3)

Back

x = 5

Front

What is the relationship between negative exponents and fractions?

Back

A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent. For example, a^(-n) = 1/(a^n).

Front

Solve: 7^(-x) = 49

Back

x = -2

Front

How can you rewrite 49 in terms of base 7?

Back

49 can be rewritten as 7^2.

Front

What is the property of exponents that allows us to equate exponents when bases are the same?

Back

If a^m = a^n, then m = n, provided that a is not equal to 0.

Front

Solve: 81^(3-x) = (1/3)^(5x-6)

Back

x = -6

Front

How do you express 1/16 as a power of 4?

Back

1/16 can be expressed as 4^(-2) because 4^2 = 16.