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