Notes Over 5.2
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Notes Over 5.2Rewriting Logarithmic Equations
364log .1 4 4
and
3 643125log .2 5
53 125
1log .3 7
7 0 1 8
1log .4 2
23
8
1
xy alog yax Rewrite the equation in exponential form.
are equivalent.
Evaluate each logarithm.
0 3
Notes Over 5.2Properties of Logarithms
.1 01log a 1 because 0 a
.2 1log aa aa 1 because
.3 xa xa log xa xa log because
.4 yx aa loglog If yx then
5loglog .5 77 xUse properties to solve.
5xx 5
33log .65x
Notes Over 5.2Graphing Logarithmic Functions
xxf 2 .7 Graph both functions on the same graph.
x y
2 4/11
012
2/1124
xxg 2logx y
4/1 22/1
124
1012
Notes Over 5.2Common and Natural Logarithms
25log .8 10
397.13.0ln .9
204.1
e
1ln .11
xy 10logUse a calculator to evaluate.
Use properties to simplify.
1ln e
xy elog xlnx log
21ln .10 881.0
13
1ln .12
3
0 0
Notes Over 5.2Graphing Logarithmic Functions
xxf ln .13 Graph the logarithmic function.
x y
2135.1
012
368.172.239.7
Inverse of xey
sticscharacteriDomain:
Range:x-int:
Inc/Dec:
asymp:
Contin:
,0 ,
1increasing
0xcontinuous
Notes Over 5.2Graphing Logarithmic Functions
2 log .14 4 xy
Graph the function.
x y
1 04 1
xy 4 of Inverse
Move curve 2 units to the left.
Asymptote: 2x
Notes Over 5.2