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As this example shows, 3 is the exponent come which the basic 2 should be elevated to produce the answer of 8,or 23 = 8. In basic terms:


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(where x > 0 andb is a positive consistent not equal to 1)
Logarithms through base 10 are referred to as common logarithms.

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when the base is not indicated, basic 10 is implied. The log
key on the graphing calculator will calculate the common (or basic 10) logarithm. 2nd log will calculate the antilogarithm or 10x
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To enter a logarithm through a different base on the graphing calculator, use the Change of base Formula:
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If your calculator has the logBASE operation template, girlfriend can enter the values as they appear in the expression. go to: math → arrowhead down to A:logBASE( Or struggle MATH, ALPHA (key), mathematics togettothe A: option.


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Logarithms with base e are referred to as natural logarithms. organic logarithms are denoted through ln.On the graphing calculator, the base e logarithm is the ln key.


once working through logarithms on your graphing calculator,you should remember the "Change of basic Formula":



1. Evaluate:
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2. Evaluate: ln 2; ln 1; ln e

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3. Evaluate:
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4. Lay out the graph the
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If you have actually the logBASE function, it deserve to be used to enter the function (seen in Y1 below). If not, use the change of basic formula (see in Y2 below).

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5. Use a graph to assistance the conclusion that the station of
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is
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A role composed with its inverse create the identification line y = x. Showing that the ingredient of these two functions is the identity line mirrors that these functions are inverses of one another. Note the bubble animation collection for Y4 to display that the straight lines in Y3 and Y4 space equivalent. You are mirroring that the ingredient of Y1(Y2) = x (the identification Function).

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6. Settle graphically:
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method 2: This problem can also be solved by setting the equation same to 0 and finding the x-intercepts, or zeros (2nd CALC, #2), that the function.

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an approach 1: Graph each side separately.The home window must be readjusted to display a adequate amount the the x-axis to locate the intersection suggest (2nd CALC, #5). The answer is x = 32.

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7. Using your graphing calculator, determine which the the following statements room true.
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a.) T b.) F c.) F d.) T e.) F f.) T
Solution for component a: (TRUE)Place the left next of the equation in Y1 and also the ideal side in Y2. Turn on the "bubble animation" to the left that the Y2. This will permit you to view the bubble floating over the graph when the equation is true. Parts b - f are solved in a comparable manner.
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detect Your means Around TABLE of components