Note:

- To solve an exponential equation, isolate the exponential term, take the logarithm of both sides and solve.

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

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

Problem 7.4g:

Answer: No Solution. There is no real number such that

Solution:

In order to solve this equation, we have to isolate the exponential term. Since we cannot easily do this in the equation's present form, let's tinker with the equation until we have it in a form we can solve.

The left side of the equation is not easily factored.
Let's see if we can use the Quadratic Formula.

Note that the equation can be rewritten as This is a quadratic
equation in If it is easier for you, substitute a number, say *p*,
in place of and rewrite the equation as let's solve this equation for *p*.

However, the initial equation did not contain *p*, therefore you have to
re-substitute for *p* and solve for x.

There are no real answers.

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 never crosses the x-axis. This means that
there are no real solutions.

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