Math Questions SetQuestion 1:3. (i) Express y as a function of x, givenClearly state the relevant logarithm rules you use.(ii) Express the following as a single natural logarithm:Clearly state the relevant logarithm rules you use.estion 2:3 log₂ (xy) - 2 log₂ (x²y) + 2 = 3 log₂ y.(-)-(-¹+ 1.

Introduction: In mathematics, logarithmic function is very significant function. This function is…

Answered: Math Questions Set Question 1: 3. (i)…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.6: Exponential And Logarithmic Equations

Problem 81SE: Newton’s Law ofCooling states that the temperatureTof an object at any time t can be described by...

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Newton’s Law ofCooling states that the temperatureTof an object at any time t can be described by theequation T=Ts+(T0Ts)ekt, where Ts is thetemperature of the surrounding environment, T0 is the initial temperature of the object, and k is thecooling rate. Use the definition of a logarithm alongwith properties of logarithms to solve the formula fortime tsuch that tis equal to a single logarithm.
Logarithmic and Exponential Forms Complete the table by finding the appropriate logarithmic or exponential from of the equation, as in Example 1.
Reaction Time For certain decisions, the time it takes to respond is a logarithmic function of the number of choices faced. One model is, R=0.17+0.44logN where R is the reaction time in seconds and N is the number of choices. a.Draw a graph of R versus N. Include values of N from 1 to 10 choices. b.Using functional notation, express the reaction if there are seven choices, and then calculate that time. c.If the reaction is to be at most 0.5 second, how many choices can there be? d.If the number of choices increases by a factor of 10, what happens to the reaction time. e.Explain in practical terms what the concavity of graph means.
Difficulty of a Task The difficulty in "acquiring a target" such as using your mouse to click on an icon on your computer screen depends on the distance to the target and the size of the target. According to Fittss Law, the index of difficulty ID is given by ID=log(2A/W)log2 where W is the width of the target and A is the distance to the center of the target. Compare the difficulty of clicking on an icon that is 5 mm wide to clicking on one that is 10 mm wide. In each case, assume that the mouse is 100 mm from the icon.
Stride Frequency of Animals Four-legged animals run with two different types of motion: trotting and galloping. An animal that is trotting has at least one foot on the ground at all times, whereas an animal that is galloping has all four feet off the ground at some point in its stride. The number of strides per minute at which an animal breaks from a trot to a gallop depends on the weight of the animal. Use the table to find a logarithmic equation that relates an animal’s weight x (in pounds) and its lowest stride frequency while galloping y (in strides per minute).

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Math Questions Set Question 1: 3. (i) Express y as a function of x, given 3 log₂ (xy²) - 2 log₂ (x²y) + 2 = 3 log₂ y. Clearly state the relevant logarithm rules you use. (ii) Express the following as a single natural logarithm: In In Clearly state the relevant logarithm rules you use. +1.