SOLVING EXPONENTIAL EQUATIONS Problem 5

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

Problem 5: Solve for x in the equation

Solution:

Step 1: Isolate the exponential term

using steps 2 through 6.

Step 2: Divide both sides of the original equation by 500:

Step 3: Subtract 1 from both sides of the above equation:

Step 4: Multiply both sides of the above equation by

Step 5: :Divide both sides of the above equation by 0.92:

Step 6: Subtract 4 from both sides of the above equation:

Step 7: Take the natural log of both sides of the above equation:

Step 8: Simplify the left side of the above equation using Logarithmic Rule 3:

Step 9: Since Ln(e) = 1, the above equation is simplified to

Step 10: Divide both sides of the above equation by -0.002:

rounded to 528.

Check: Check the graph, it should cross in one place very close to x = 528. You can also substitute the number in the original equation and check to see if the left side of the equation then equals the right side of the equation.

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