SOLVING EXPONENTIAL EQUATIONS - Example
To solve an exponential equation, take the log of both sides, and
solve for the variable.
Example 9: Solve for x in the equation
- Step 1: If you graph
you will note that the graph crosses the x-axis at the origin. This means
there is only one solution and that solution is 0.
- Step 2: Isolate the exponential term using steps 2 through 7.
- Step 3: Divide both sides of the original equation by 3: The expression
can now be written
- Step 4: Take the cube root of both sides:
- Step 5: Add 5 to both sides:
- Step 6: Divide both sides by 7:
- Step 7: By now you should recognize that the value of x has to be 0. If you do not, take the natural log of both sides:
which can be written .
Check: Let's check the answer with the original problem. When we substitute the 0 for the value of x in the left side of the equation, we get
We have proved our answer.
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