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.
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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