SOLVING EXPONENTIAL EQUATIONS - Problem 2

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

Problem 2: Solve for x in the equation

Solution:

Step 1: Isolate the exponential term

using steps 2 through 4.

Step 2: Multiply both sides of the original equation by

Step 3: Divide both sides of the above equation by 5:

Step 4: Subtract 2 from both sides:

Step 5: Since the base is 7, take

of both sides:

Step 6: Simplify the left side of the above equation using Logarithmic Rule 3:

Step 7: We know that

(that's why we choose

). Therefore, the left side of the equation can be simplified to

Step 8: Divide both sides of the above equation by 3:

is the exact answer.

displaymath87

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

Close enough to 5. Remember it will not check directly because we rounded the answer. If you choose to round to only 2 or 3 decimals, the difference between the check answer and 5 would be greater.

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Author: Nancy Marcus