SOLVING EXPONENTIAL EQUATIONS

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 7.3d

Answer:No solution.

Solution:

Note that the domain is the set of real numbers such that or

Isolate the exponential term in the equation .

Divide both sides of the equation by 56

Square both sides of the equation.

Take the natural log of both sides of the equation

Since 0.74247042592 is not , there is not 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 never crosses the x-axis.. This means that there are no real solutions.

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