1. 8-3 Logarithmic Functions as Inverses
10/19/17

2. A logarithm is the inverse to an exponential function.
23 = 8 written as a logarithm is: log2 8 = 3.
Log2 8 = x is an equation that is basically asking, “2 to what power is 8?”
When you see log2 8 = x, think: 2x = 8
Log2 8 is read “the log of 8 base 2” or “the log base 2 of 8”
General form: logb y = x means bx = y
Logs are very useful in science & mathematics, especially calculus (the “natural” log (base e). Uses of logs you may have heard of but didn’t realize they were logs: the Richter scale, decibels, pH, & musical intervals.
Let’s evaluate some logarithms…

3. Evaluate:
log3 9 = x
x = 2 (since 32 = 9)
log2 32 = x
x = 5 (since 25 = 32)
log9 729 = x
x = 3 (since 93 = 729)
log = x
x = 3 (since 103 = 1000)
log10 10 = x
x = 1 (since 101 = 10)
Logs base 10 are called the common log. A log with no base written is understood to be base 10.
log .1 = x
x = -1 (since 10-1 = .1)

4. Assignment: Page 442 #6 – 25 Write in logarithmic form: 53 = 125
Evaluate:
102 = 100
log 100 = 2
log64 1/32 = ?
64x = 1/32
24 = 16
log2 16 = 4
(26)x = same base!!
54 = 625
log5 625 = 4
26x = 2-5
6x = -5
x = -5/6
Assignment: Page 442 #6 – 25