# Logarithmic Functions Worksheet - Excel by aqs59823

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• pg 1
```									Graphs of Logarithmic Functions
(Based on Example 2 in the text.)

In this worksheet we graph two logarithmic functions, the base 2 logarithm
and the base 1/2 logarithm. Notice that the formula we use for the base 2 logarithm,
which you can see by clicking on cell B21, is LOG(X)/LOG(2). We are taking advantage
of the change-of-base formula to calculate the base 2 logarithm using the base 10 logarithm,
which is what LOG calculates. Actually, Excel allows you to add a second argument to LOG
to specify the base, so we could have used the formula LOG(X,2) instead.
Try other bases. How does the base affect the shape of the graph?

X              Y1            Y2                       Xmin         Xmax           NumSteps DeltaX
0      #NUM!         #NUM!                          0              3          100              0.03
0.03   -5.05889369   5.058893689
0.06   -4.05889369   4.058893689
0.09   -3.47393119   3.473931188          6
0.12   -3.05889369   3.058893689
0.15   -2.73696559   2.736965594          4
0.18   -2.47393119   2.473931188
0.21   -2.25153877   2.251538767
2
0.24   -2.05889369   2.058893689
0.27   -1.88896869   1.888968688
0.3   -1.73696559   1.736965594
0
0.33   -1.59946207    1.59946207              0      0.5          1       1.5       2       2.5
0.36   -1.47393119   1.473931188         -2
0.39   -1.35845397   1.358453971
0.42   -1.25153877   1.251538767         -4
0.45   -1.15200309   1.152003093
0.48   -1.05889369   1.058893689         -6
0.51   -0.97143085   0.971430848
X
0.54   -0.88896869   0.888968688
0.57   -0.81096618   0.810966176
0.6   -0.73696559   0.736965594
0.63   -0.66657627   0.666576266
0.66   -0.59946207    0.59946207
0.69   -0.53533173   0.535331733
0.72   -0.47393119   0.473931188
0.75    -0.4150375   0.415037499
0.78   -0.35845397   0.358453971
0.81   -0.30400619   0.304006187
0.84   -0.25153877   0.251538767
0.87   -0.20091269   0.200912694
0.9   -0.15200309   0.152003093
0.93   -0.10469738   0.104697379
0.96   -0.05889369   0.058893689
0.99   -0.01449957    0.01449957
1.02    0.02856915   -0.02856915
1.05    0.07038933   -0.07038933
1.08    0.11103131   -0.11103131
1.11   0.15055968    -0.15055968
1.14   0.18903382    -0.18903382
1.17   0.22650853    -0.22650853
1.2   0.26303441    -0.26303441
1.23   0.29865832    -0.29865832
1.26   0.33342373    -0.33342373
1.29   0.36737107    -0.36737107
1.32   0.40053793    -0.40053793
1.35   0.43295941    -0.43295941
1.38   0.46466827    -0.46466827
1.41   0.49569516    -0.49569516
1.44   0.52606881    -0.52606881
1.47   0.55581616    -0.55581616
1.5    0.5849625     -0.5849625
1.53   0.61353165    -0.61353165
1.56   0.64154603    -0.64154603
1.59   0.66902677    -0.66902677
1.62   0.69599381    -0.69599381
1.65   0.72246602    -0.72246602
1.68   0.74846123    -0.74846123
1.71   0.77399633    -0.77399633
1.74   0.79908731    -0.79908731
1.77   0.82374936    -0.82374936
1.8   0.84799691    -0.84799691
1.83   0.87184365    -0.87184365
1.86   0.89530262    -0.89530262
1.89   0.91838623    -0.91838623
1.92   0.94110631    -0.94110631
1.95   0.96347412    -0.96347412
1.98   0.98550043    -0.98550043
2.01    1.0071955     -1.0071955
2.04   1.02856915    -1.02856915
2.07   1.04963077    -1.04963077
2.1   1.07038933    -1.07038933
2.13   1.09085343    -1.09085343
2.16   1.11103131    -1.11103131
2.19   1.13093087    -1.13093087
2.22   1.15055968    -1.15055968
2.25      1.169925      -1.169925
2.28   1.18903382    -1.18903382
2.31   1.20789285    -1.20789285
2.34   1.22650853    -1.22650853
2.37   1.24488706    -1.24488706
2.4   1.26303441    -1.26303441
2.43   1.28095631    -1.28095631
2.46   1.29865832    -1.29865832
2.49   1.31614574    -1.31614574
2.52   1.33342373    -1.33342373
2.55   1.35049725    -1.35049725
2.58   1.36737107    -1.36737107
2.61   1.38404981    -1.38404981
2.64   1.40053793    -1.40053793
2.67   1.41683974    -1.41683974
2.7   1.43295941    -1.43295941
2.73   1.44890095    -1.44890095
2.76   1.46466827    -1.46466827
2.79   1.48026512    -1.48026512
2.82   1.49569516   -1.49569516
2.85   1.51096192   -1.51096192
2.88   1.52606881   -1.52606881
2.91   1.54101915   -1.54101915
2.94   1.55581616   -1.55581616
2.97   1.57046293   -1.57046293
3    1.5849625    -1.5849625
3   3.5

```
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