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 5000:

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

 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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Marcus
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