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

How do you solve the equation 2^(x+6) = 32?

Back

Convert 32 to a power of 2: 32 = 2^5. Therefore, x + 6 = 5, leading to x = -1.

Front

What is the base of an exponential function?

Back

The base is the constant value that is raised to a power, such as in a^x.

Front

How do you rewrite 1/125 as a power of 5?

Back

1/125 = 5^(-3).

Front

What is the solution to the equation 3^(2x) = 27?

Back

Convert 27 to a power of 3: 27 = 3^3. Therefore, 2x = 3, leading to x = 3/2.

Front

What is the first step in solving exponential equations?

Back

Identify if both sides can be expressed with the same base.

Front

How do you solve the equation 36 = 6^x?

Back

Rewrite 36 as 6^2, so x = 2.

Front

What is the logarithm of a number?

Back

The logarithm is the exponent to which a base must be raised to produce that number.

Front

What is the relationship between exponents and logarithms?

Back

If a^b = c, then log_a(c) = b.

Front

How do you solve for x in the equation 5^(a+2) = 1/125?

Back

Rewrite 1/125 as 5^(-3). Therefore, a + 2 = -3, leading to a = -5.