Transcript 8.4 – Solving Logarithmic Equations and Inequalities

6.4 – Solving Logarithmic
Equations and Inequalities
Objective: TSW solve logarithmic
equations and inequalities.
Logarithmic equation – an equation that contains
one or more logarithm.
REMEMBER…
Logarithmic form: y = logb x
Exponential Form: by = x.
REMEMBER… For x > 0 and b > 0, and b = 1
So…x and b MUST be positive and b can never equal
1 (this is why we have asymptotes in our graphs)
To Solve a Logarithm with Only ONE log….
1. Rewrite the logarithm
2. Break down each side so bases are equal
3. Solve for the exponent.
4. Check Solution to be sure the number within the log
is positive.
To Solve a Logarithm with a log on each side…
1. Make sure the log and the base are IDENTICAL.
2. If the logs are identical, then the numbers within in
the log are identical so set them equal.
3. Solve for x…YOU MAY HAVE TO FACTOR!
4. Check Solution to be sure x is positive!
Examples: Solve Each Equation
1. log 3 x  3
2. log 36 x  3 / 2
3. log x 4  5 / 2
4. log x 36  1 / 2
5. log 16 (1 / 2)  x
6. log 25 (5)  x
Examples…Solve Each Equation
7.
log 5 (12 x  5)  log 5 (8x  9)
Examples…Solve Each Equation
8.
log 12 ( x  7)  log 12 ( x  5)
2
Examples…Solve Each Equation
2
log
(
x
 4 x)  log 9 (3x  10)
9.
9
Homework!
pgs. 504-507 #’s 1-17(odds), 23-29(odds), 4957(odds)