Solving Equations with One Log Term

Example 1

Solve: log_x 100 = 2.

Since x is the base, it must be positive. Therefore, -10 is not a solution. The solution is x = +10.

So, log₁₀100 = 2. The solution checks since 10² = 100. You may also check the solution on a calculator.

Example 2

Solve:

Solution	logx 8
Rewrite in exponential form. Rewrite using a radical. Square both sides.	x1/2 x	= 8 = 8 = 64

So,

Note:

The solution of is x = 64.

Here is a check.

Example 3

Solve:

Solution
Rewrite in exponential form. Rewrite x-2 as .
Cross multiply. Take the square root of each side. Simplify.	x2 = 16 x = ± x = ± 4

So, We leave the check to you.