Explanation Given information: The logarithmic function, f ( x ) = log 1 / 6 x Concept used: The equivalent exponential form of a logarithm for a > 0 , x > 0 , a ≠ 1 is given by log b x = y if and only if x = b y In a rectangular coordinate system any point is represented as ( x , y ) . It indicates that the point is at a horizontal distance of x units and vertical distance of y units from the origin ( 0 , 0 ) . A point in the first quadrant be of the form ( + , + ) . A point in the second quadrant be of the form ( − , + ) . A point in the third quadrant be of the form ( − , − ) . A point in the fourth quadrant be of the form ( + , − ) . Calculation: To plot the graph of the given logarithmic function, first we will convert it into equivalent exponent form. Let y = f ( x ) , so we have y = f ( x ) ⇒ y = log 1 / 6 x ⇒ x = ( 1 6 ) y Now we will find some ordered pairs that satisfy above equation by taking some random values of y and find the corresponding x -values. Then we plot these points on rectangular coordinate system and connect with a smooth curve. The domain of the logarithmic function is all positive real numbers greater than zero and range is all real numbers

2nd Edition

ISBN: 9780135257500

Author: Martin-Gay

Publisher: PEARSON

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System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 19.5, Problem 83ES

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The graph of the logarithmic function f(x)=log1/6x .

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Chapter 19.5, Problem 82ES

Chapter 19.5, Problem 84ES

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Chapter 19 Solutions

Algebra Foundations

Ch. 19.1 - Prob. 1VRVC Ch. 19.1 - Prob. 2VRVC Ch. 19.1 - Prob. 3VRVC Ch. 19.1 - Prob. 4VRVC Ch. 19.1 - Prob. 5VRVC Ch. 19.1 - Prob. 6VRVC Ch. 19.1 - Prob. 1ES Ch. 19.1 - Prob. 2ES Ch. 19.1 - Prob. 3ES Ch. 19.1 - Prob. 4ES

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The graph of the logarithmic function f ( x ) = log 1 / 6 x .

Solution Summary: The author describes the graph of the logarithmic function f(x)=log1/6x.

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The graph of the logarithmic function f(x)=log1/6x .

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