1. To solve a logarithmic equation, rewrite the equation in exponential form and solve for the variable.
Example 1: Solve for x in the equation Ln(x)=8.
Solution:
and the approximate answer is
Check: You can check your answer in two ways. You could graph the function Ln(x)-8 and see where it crosses the x-axis. If you are correct, the graph should cross the x-axis at the answer you derived algebraically.
You can also check your answer by substituting the value of x in the initial
equation and determine whether the left side equals the right side. For
example, if Ln(2,980.95798704)=8, you are correct. It does, and you are correct.
Example 2: Solve for x in the equation 7Log(3x)=15.
Solution:
can now be written
is the exact answer and is the approximate answer.
Check: You can check your answer in two ways: graphing the function
or substituting the value of x into the original equation. If you choose graphing, the x-intercept should be the same as the answer you
derived ( ).
If you choose substitution, the value of the left side of the original
equation should equal the value of the right side of the equation after you
have calculated the value of each side based on your answer for x.
Example 3: Solve for x in the equation
Solution:
Another way of looking at the equation in Step 3 is to realize that if Ln(a) = Ln(b), then a must equal b. In the case of this problem, then
Check: You can check your answer by graphing the function
and determining whether the x-intercept is also equal to 9. If it is, you
have worked the problem correctly.
You could also check your answer by substituting 9 for x in the left and
right sides of the original equation. If, after the substitution, the left
side of the equation has the same value as the right side of the equation,
you have worked the problem correctly.
If you would like to review another example, click on Example.
Work the following problems. If you wish to review the answer and the
solution, click on Answer.
Problem 1: Solve for x in the equation
Problem 2: Solve for x in the equation
Problem 3: Solve for x in the equation
Problem 4: Solve for x in the equation
Problem 5: Solve for x in the equation
Problem 6: Solve for x in the equation
Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.
Author: Nancy Marcus