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 an exponential equation with the same base?

Back

To solve an exponential equation 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 81^(3-x) = (1/3)^(5x-6)?

Back

The first step is to express both sides of the equation with the same base. Here, 81 can be written as 3^4 and (1/3) as 3^(-1).

Front

What is the solution to the equation 10^(2x+4) = 100000?

Back

The solution is x = 1/2.

Front

How can you rewrite 27^(x-4) in terms of base 3?

Back

27 can be rewritten as 3^3, so 27^(x-4) becomes (3^3)^(x-4) = 3^(3(x-4)).

Front

What is the value of x in the equation 3^(2x) = 27^(x-4)?

Back

The value of x is 12.

Front

How do you solve the equation 2^(-m) = 2^(3m-3)?

Back

Set the exponents equal to each other: -m = 3m - 3, then solve for m.

Front

What is the solution to the equation 2^(-m) = 2^(3m-3)?

Back

The solution is m = 3/4.

Front

How do you solve (1/8)^x = 2^3?

Back

Rewrite (1/8) as 2^(-3), so the equation becomes (2^(-3))^x = 2^3, leading to -3x = 3.

Front

What is the solution to the equation (1/8)^x = 2^3?

Back

The solution is x = -1.