Note:

If you would like an in-depth review of logarithms, the rules of logarithms, logarithmic functions and logarithmic equations, click on logarithmic functions.

Solve for x in the following equation.

**Problem 8.5a:**

**Answers:**

**Solution:**

The above equation is valid only if each of the three terms is valid. The
term
is valid if *x*>2. The term
is valid if *x*>-4. The term
is valid if *x*>1. Therefore, the equation is valid when the
domain is the set of real numbers is greater than2, greater than -4, and
greater than1. This means that the equation is valid if we restrict the
domain to the set of real numbers greater than2.

Simplify the equation and solve.

The exact answer is The approximate answer is

These answer may or may not be the solution to the original equation. You must it in the original equation, either by numerical substitution or by graphing.

**Numerical Check:**

- Check the answer by substituting in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.

Left Side:

Right Side:

The left side does not equal the right side exactly because we rounded the
numbers. However, it is close enough to verify our answers.Since the left
side of the original equation is equal to the right side of the original
equation after we substitute the value 2.192582 for x, then
*x*=2.192582is a solution.

**Graphical Check:**

You can also check your answer by graphing
(formed by subtracting the right side of the original equation from the left
side). Look to see where the graph crosses the x-axis; that will be the real
solution. You may have to modify the equation for your calculator first.
Rewrite f(x) as

Note that the graph crosses the x-axis at 2.192582. This means that 2.192582 is the real solution.

**
If you would like to review the solution to problem 8.5b, click on solution.
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