## 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. under Algebra.

Solve for x in the following equation.

Example 4:

Isolate the exponential term.

Note that the base is e, not Multiply both sides of the equation by

Take the natural logarithm of both sides of the equation

Your exact answer may differ dependent how what logarithm you used to solve the problem. However, all forms of the correct answer will simplify to the same approximate answer.

When solving the above problem, you could have used any logarithm. For example, let's solve it using the logarithmic with base 14. Take the of both sides of the equation

Check these answers in the original equation.

Check the solution by substituting 1.11693268486 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: 0.625

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value 1.11693268486 for x, then x=1.11693268486 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 1.11693268486.. This means that 1.11693268486 is the real solution.

If you would like to test yourself by working some problems similar to this example, click on Problem

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Author: Nancy Marcus