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DISCUSS: The Height of the Graph of a Logarithmic FunctionSuppose that the graph of $y=2^{x}$ is drawn on a coordinateplane where the unit of measurement is an inch.\begin{equation}\begin{array}{l}{\text { (a) Show that at a distance } 2 \text { ft to the right of the origin the }} \\ {\text { height of the graph is about } 265 \text { mi. }} \\ {\text { (b) If the graph of } y=\log _{2} x \text { is drawn on the same set of }} \\ {\text { axes, how far to the right of the origin do we have to go }} \\ {\text { before the height of the curve reaches } 2 \mathrm{ft} \text { ? }}\end{array}\end{equation}

265 miles

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

Campbell University

Oregon State University

Idaho State University

Lectures

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Discuss: The Height of the…

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The Height of the Graph of…

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Discuss a DISCOVER: The He…

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DISCUSS = DISCOVER: The He…

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Suppose that the graph of …

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Suppose the graphs of $f(x…

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Suppose the graphs of $ f(…

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Graph the logarithmic func…

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Graph each logarithmic fun…

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Match the logarithmic func…

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Graphing Logarithmic Funct…

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Sketch the graphs of $y=\l…

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Explain how the graph of t…

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For the following exercise…

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Sketch the graph of the fu…

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So for this problem, we can we can solve a algebraic with Well, if we want the the height to be 265 miles. Well, well, let's say we have 265 miles and we want to convert that two inches. So we have 265 miles times 5280 feet per mile. And then we have we have times 12 inches per feet. Perfect. And so if we multiply this, what we get is is to 65 times 5280 times 12. So we get approximately approximately 17 17 million, 17 million. And it's all right this as 17 to 17 times times 10 to the power of six. So this is also equal to 17 times 10 to the power of six. Well, we know that we should have approximately this value. We should have approximately this value if we have, if we move to if we move two feet in the X direction and so so acts should be two times 12. So two to the 24 we plug in two to the 24 in our calculator. We do see that this is in fact, approximately 17 times 10 to the six power that we have. This is true. This is true. And so for part B, Now we have this. Now we want our our height to reach two feet. So are why should be 24. So we have 24 is equal to log base two of X, long based two of X. So in this dysentery we have two to the 24 is equal to X. And so now now we have X is approximately 17 times 10 to the six power. So these are our solutions.

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