1. Section 4 – Logarithmic Functions
Chapter 11
Section 4 – Logarithmic Functions

2. Logarithmic Function
The logarithmic function y = logax, where a>0, is the inverse of the exponential function y = ax.
So, y = logax if and only if x = ay.
EX 1: Write in exponential form:
2/3 = log12525
EX 2: Write in exponential form:
1/3 = log82

3. More Examples Write each equation in logarithmic form. EX 3: 64 = 43

4. One More Example
EX 5: Evaluate the expression log71/49

5. Properties of Logs PROPERTY DEFINITION EXAMPLE Product
logbmn = logbm + logbn
log39x = log39 + log3x
Quotient
logb(m/n)=logbm – logbn
log1/4(4/5) = log1/4(4)-log1/4(5)
Power
logbmp = p(logbm)
log28x = x(log28)
Power of Equality
If logbm = logbn, then m=n
log8(3x-4) = log8(5x+2) so, 3x-4 = 5x+2

6. More Examples EX 6: Solve the equation: logp641/3 = ½
log4(2x+11) = log4(5x-4)
EX 8: Solve the equation:
log11x + log11(x+1) = log116

7. Assignment
Chapter 11, Section 4
pgs #20-52E,60,64