Exponential and Logarithmic Functions 224 Chapter 3 OCondensing a Logarithmic Expression In Exercises 61-76, condense the expression to the logarithm of a single quantity. ON 83. 62. logs 8 - log, t 61. In 3 + In x 63. log,(z – 2) 64. -4 In 3x 66. 2 log, x + 4 log2 y 65. log, 5x – 4 log; x 67. log x + 2 log(x + 1) 84. 68. 2 In 8 – 5 In(z - 4) 69.) log x - 2 log y + 3 log z 70. 3 log, x + i log, y - 4 log; z 71. In x - [In(x + 1) + In(x – 1)] 72. 4[In z + In(z + 5)] – 2 In(z – 5) 73. [2 In(x + 3) + In x- In(x² – 1)] 74. 2[3 In x - 75. [logs y + 2 log3(y + 4)] – log3(y – 1) 76. [log,(x + 1) + 2 log,(x – 1)] + 6 log4 x 85. In(x + 1) – In(x – 1)] 86. Comparing Logarithmic Quantities In Exercises 77 and 78, determine which (if any) of the logarithmic expressions are equal. Justify your answer. log, 32 77. 32 log2 log, 32 - log, 4 4' log, 4' 78. log,/70, log, 35, + log , V10 •• Sound Intensity In Exercises 79-82, use the following information. The relationship between the number of decibels B and the intensity of a sound
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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