##
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 functions.

Solve for x in the following equation.

**
Problem 9.1c:**

**Answer:**
There are an infinite number of solutions:
are the exact solutions, and
are the approximate solutions.

**Solution:**
To solve for x, first isolate the tangent term.

If we restrict the domain of the tangent function to
,
we can use the arctangent function to solve for x.

The period of tangent function is
This means that the values will
repeat every
radians. Therefore, the solutions are
where n is an integer.

These solutions may or may not be the answers to the original problem. You
much check them, either numerically or graphically, with the original
equation.

**Numerical Check:**

Check the answer .
*x*=1.5458015

- Left Side:

- Right Side: 20

Since the left side equals the right side when you substitute 1.5458015for x, then 1.5458015 is a solution.

**Graphical Check:**

Graph the equation

Note that
the graph crosses the x-axis many times indicating many solutions.

Note the graph crosses at 1.5458015 (one of the solutions).
Since the period of the function is
,
the
graph crosses again at
1.5458015+3.1415924.687394 and again at
,
etc.

**
If you would like to review the solution to problem 9.1d, click on solution.
**

If you would like to go back to the equation table of contents, click on
contents.

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