Solving Exponential Equations

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

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

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

1/125 = 5^(-3).

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

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

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

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

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

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