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6:19 20:56 Suggested clip Graphing Logarithmic Functions With Transformations, Asymptotes YouTubeStart of suggested client of suggested clip Graphing Logarithmic Functions With Transformations, Asymptotes
log2 x = log(x)/log(2) 2. How do transformations affect the logarithmic graph? — They shift graph up/down/left/right. Y=log(x-h)+h k shifts graph vertically and h shifts graph horizontally.
0:22 12:51 Suggested clip Lesson 8.3 — Graphing Transformations of Logarithmic Functions YouTubeStart of suggested client of suggested clip Lesson 8.3 — Graphing Transformations of Logarithmic Functions
5:00 18:03 Suggested clip Master Graphing Logarithmic Equations with multiple transformationsYouTubeStart of suggested client of suggested clip Master Graphing Logarithmic Equations with multiple transformations
The log transformation is, arguably, the most popular among the different types of transformations used to transform skewed data to approximately conform to normality. If the original data follows a log-normal distribution or approximately so, then the log-transformed data follows a normal or near normal distribution.
The log transformation can be used to make highly skewed distributions less skewed. This can be valuable both for making patterns in the data more interpretable and for helping to meet the assumptions of inferential statistics. Figure 1 shows an example of how a log transformation can make patterns more visible.
For the log transformation, you would back-transform by raising 10 to the power of your number. For example, the log transformed data above has a mean of 1.044 and a 95% confidence interval of ±0.344 log-transformed fish. The back-transformed mean would be 101.044=11.1 fish.
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