WEBVTT
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For which values of π is the function π of π₯ is equal to log base π of π₯ decreasing?
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This question can be answered directly from our definition of the logarithmic function.
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We recall that a logarithmic function is the inverse of an exponential function.
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And log base π exists if π is greater than zero and not equal to one.
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We can go one stage further by recalling that if π is greater than zero and less than one, π of π₯ decreases throughout its domain.
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However, if π is greater than one, the function log base π of π₯ increases throughout its domain.
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In this question, weβre asked for the values of π for which the function is decreasing.
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And we can therefore conclude that the function π of π₯ is equal to log base π of π₯ is decreasing when π exists on the open interval from zero to one.
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It is worth noting that the graph of the function π¦ is equal to log base π of π₯, where π exists on the open interval between zero and one, is as shown.
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This confirms that the function is indeed decreasing over its entire domain.