Logarithmic Equations Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

Remember that the composition of a function and its inverse returns the starting value.

A logarithmic equation can be solved using the properties of logarithms along with the use of a common base.

Properties of Logs:

 To solve most logarithmic equations: 1.  Isolate the logarithmic expression. (you may need to use the properties to create one logarithmic term) 2.  Rewrite in exponential form (with a common base) 3.  Solve for the variable.
Do you see composition of a function and its inverse at work in the last statements?  Find out more about
exponential and log functions.

Examples:

1.
 ANSWER: • Isolate the log expression • Choose base 10 to correspond with log (base 10) • Apply composition of inverses and solve.
2.
 ANSWER: • Remember that ex and ln x are inverse functions.
3.
4.
 ANSWER: • Isolate the logarithmic expression first.
5.

 ANSWER: • Use the log property to express the two terms on the left as a single term.• Remember that log of a negative value is not a real number and is not considered a solution.
6.
7. Using your graphing calculator, solve for x to the nearest hundredth.

 Method 2:  Place the left side of the equation into Y1 and the right side into Y2.  Under the CALC menu, use #5 Intersect to find where the two graphs intersect.

Method 1:  Rewrite so the equation equals zero.

Find the zeros of the function.

Both values are solutions, since both values allow for the ln of a positive value.

 How to use your TI-83+/84+ graphing calculator  with logarithms. Click calculator.

 Topic Index | Algebra2/Trig Index | Regents Exam Prep Center Created by Donna Roberts