# SOLVING EXPONENTIAL EQUATIONS - Problem 1 To solve an exponential equation, take the log of both sides, and solve for the variable. Problem 1: Solve for x in the equation Solution:

Step 1: Isolate the exponential term in the equation using steps 2 through 5.

Step 2: Subtract 8 from both sides of the above equation: Step 3: Since the base is 5, take the log to base 5 of both sides: Step 4: Simplify the left side of the equation using Logarithmic Rule 3: Step 5: Simplify the left side: We know that (that's why we choose log with a base 5). Therefore, the left side of the equation can be simplified to Step 6: Subtract 3 from both sides of the above equation: Step 7: Divide both sides of the above equation by 2: is the exact answer. is an approximate answer.

Check: Let's check the approximate answer with the original problem. When we substitute the above value of x in the left side of the equation, we get If you would like to work another problem, click on Next Problem. [Next Problem] [Menu Back to Solving EE]

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