solve logarithmic equations log 2x = 3
Post on 03-Dec-2021
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Solve Logarithmic Equations
Solve log 2 2x = 3
2x = 23
2x = 8
x= 4 Check the solution x= 4!!!
Property of Equality for Logarithmic Functions
log b x =log by If and only if
log b x =log b 5 Example
Check the solution!
Solve Logarithmic Equations
Solve log 2 (x+17) = log 2 (3x+23)
x+ 17 = 3x + 23
x– 3x = 23 - 17
- 2x = 6
x = -3
Check the solution x= -3!!!
Property of Inequality for Logarithmic Functions
b > 1 x > 0 log b x > y
then x > by
log 3 x > 4 Example x > 34 x > 81
log b x < y x < by
Solution set: { x / x > 81}
Property of Inequality for Logarithmic Functions
If b > 1
log b x >log by If and only if
x > y
log 6 x >log 6 5 Example x > 5
log b x <log by x < y
Solve Logarithmic Inequalities
Solve log 4 (x+3) > log 4 (2x+1)
The solution set is { x/ -1/2 <x < 2}
.
x + 3 > 2x + 1 2 > x
The domains for logs are x+3>0, x>-3 and 2x+1>0, x>-1/2 with x<2
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