SOLVING EXPONENTIAL EQUATIONS - Problem 3

To solve an exponential equation, take the log of both sides, and solve for the variable.

Problem 3: Solve for x in the equation

Solution:

Step 1: If you graph the left side of the above equation, you will note that the graph crosses the x-axis in two places, once to the left of the y-axis and once to the right of the y-axis. This means that there will be one negative real solution and one positive real solution.

Step 2: Write the equation in quadratic form and factor:

Step 3: The only way a product of two factors is zero is when one or both of the factors is equal to zero.

Step 4: If

and

. Take the natural log of both sides.

is the exact answer and x=0.916290731874 is an approximate answer.

Step 5: If

and

Take the natural log of both sides. and

is the exact answer and

is an approximate answer.

Check: Let check both answers with the original problem. If when the value of x is substituted in the left side of the equation, the value of the left side of the equation equals the right side of the equation (in this case 0), you have found the correct answer. You could also check the values of x with the x-intercepts on your graph. They should be the same.

They do and you have worked the problem correctly.

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