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

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