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
- 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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