Note:
If you would like an in-depth review of exponents, the rules of exponents, exponential functions and exponential equations, click on exponential function.
Solve for x in the following equation.
Problem 7.6c:
Answer:
Exact answer: Approximate answer:
Solution:
The first step is to isolate
Subtract 8 from both sides of the equation.
Divide both sides of the equation by 25.
The next step is to isolate the variable x.
Take the natural logarithm of both sides of the equation..
The exact answer is and the approximate answer is
Check the solution by substituting in the
original equation for x. If the left side of the equation equals the right
side of the equation after the substitution, you have found the correct
answer.
Right Side:
You can also check your answer by graphing the function (formed by subtracting the right side of the
original equation from the left side). Look to see where the graph crosses
the x-axis; that will be the real solution. Note that the graph crosses the
x-axis at -0.229335. This means that -0.229335 is the real solution.
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