Name: ____________________
Pre- Calculus 12 H.
Date: _____________
Chapter 8 – Logarithmic Functions
8.4 A – Solving Logarithmic Equations
A logarithmic equation contains one or more logarithms
-You can use the definition of a logarithm to help you solve logarithmic equations
Ex. State the restrictions on x for each of the following equations:
b) log 3 ( x  4)  log 5 (3  x)  log 2
a) log 2 ( x  2)  1
When solving equations involving logarithms, there are two general forms:
1) log c L  log c R

If you can simplify both sides to a single logarithm with the same base,
then you can equate the contents of the logarithms!
2) log c L  M

If you have a logarithm equal to a numerical value, re-write in exponential
form!
Note: When giving final solutions, we must always be aware of restrictions!
Solve 5( x4)  3(42 x1 )
Example 1:
Solve each of the following and check your solution(s).
a) log 2 x  log 2 ( x  2)  3
b) log 5 (2 x  1)  log 5 ( x  2)  1
4 x 1
 8x
Example 2: 1 Solve 2
a) Using laws of exponents

b) Using logarithms
Example 3: Solve each of the following and check your solution(s).
a) log( x  6)  log( x  2)  log 5
b) log 3 (2 x  4)  log 3 ( x  1)  log 3 8
Example 4: Solve.
a) log 3 ( x  1)  log 3 x  0
Example 5: Solve 2log ( x )  log4(4 x3)  1
4
2
b) log x   log x  3
2
b) Determine the point of intersection
f ( x)  log2 (2 x  2) & g ( x)  5  log2 ( x 1)
Assignment: p. 412 #1, 3-6, 8-10.. Bonus 3log5( x2 y)  log5( y)  log5( x)  log5(14 x13 y) Calculate  x 
 y