1. To solve a logarithmic equation, rewrite the equation in exponential form and solve for the variable.
Example 4: Solve for x in the equation
Solution:
Therefore, the problem is valid if we restrict the domain (values of x) to any real numbers x < - 2 or x > - 1. You can also graph the function
and note that there is a graph to the right of - 1 and to the left of - 2; there is no graph between these values. Note that the graph has two intercepts, one positive and one negative. The graph crosses the x-axis between 8 an 9, so you know one answer will be between 8 and 9. The graph also crosses the x-axis between - 11 and - 12, so you one answer will be between these two numbers.
which gives
Check: You can check your answer in two ways. You could graph the function
and see where it crosses the x-axis. If you are correct, the graph should
cross the x-axis at 8.512492197 and - 11.15124921973.
You can also check your answer by substituting the values of x in the
initial equation and determining whether the left side of the equation
equals the right side of the equation after the substitution.
If you would like to review another example, click on Example.
Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.
Author: Nancy Marcus