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SOLVING LOGARITHMIC EQUATIONS

Note:

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

**Solve for x in the following equation.**

**Problem 1:**

**Answer:**2

**Solution:**

The above equation is valid only if all of the terms are valid. The first
term is valid if *x*>0, the second term is valid if
*x* > -2, and the third term is valid if
Therefore, the equation is valid when all three of these conditions are met,
or when *x* > 0. The domain is the set of real numbers greater than 0.**
**

Simplify both sides of the equation using the rules of logarithms.

Recall that if that *a* = *b*. Therefore, if

Solve for x.

The exact answer is

Check the answer *x *= 2 by substituting 2 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:

Since the left side of the original equation is equal to the right side of
the original equation after we substitute the value 2 for x, then *x* = 2 is
a solution.

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. Note that the graph crosses the
x-axis at 2. This means that 2 is the real solution.

**
If you would like to review the solution to problem 8.3b, click on solution.
**

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