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The justification of the third step in her proof of the property of logarithms is;
; Power rule of exponents
<h3>What are properties of Logarithms?</h3>
From the full question, the second step stopped at;
![log_{b} (b^{x} . b^{y} )](https://tex.z-dn.net/?f=log_%7Bb%7D%20%28b%5E%7Bx%7D%20.%20b%5E%7By%7D%20%29)
Now, according to Power Rule for Exponents we know that (a^m)ⁿ = a^(m*n). That means that to raise a number with an exponent to a power, we will multiply the exponent times the power.
Thus,
will give us
using power rule of exponents
Read more about Properties of Logarithms at; brainly.com/question/14765705
The result of the identification of the graphs is presented as follows;
- <u>Graph A is the graph of the acceleration </u>function
- <u>Graph B is the graph of the velocity </u>function
- <u>Graph C is the graph of the position</u> function
The reasons why the above matching of the graphs are correct are given as follows;
<em>Question: Please find attached, a graph that is related to the question</em>
<em />
From the graphs, we have;
When graph <em>A</em> is negative, the slope of graph <em>B</em> is negative, and the function of graph <em>B </em>is reducing
When graph <em>A </em>is zero, graph <em>B</em> is horizontal
When graph <em>A </em>is at its peak, the slope of graph <em>B </em> is increasing at its fastest rate. Similarly, when graph <em>A</em> is at is lowest point, <em>B</em> is reducing the fastest
Therefore;
- <u>Graph </u><u><em>A </em></u><u>represent the graph of the acceleration</u>, and <u>graph </u><u><em>B</em></u><u> represent the graph of the velocity</u>
<u />
Graph <em>C</em> is reducing only when graph <em>B</em> is negative, and is increasing when <em>B</em> is positive
Therefore;
- <u>Graph </u><u><em>C</em></u><u> is the position graph</u>
Learn more about position, velocity, and acceleration time graphs here;
brainly.com/question/19723617