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Topic:
Logarithmic Misconceptions
Essay Instructions:
Please read M5143 M4 lecture transcript, M4 discussion prompt, discussion directions, discussion essay example, then complete an essay
Give an example of an exponential equation whose solution is a negative number. How could you plot the graph of a logarithmic function without starting with the exponential graph?
Describe mathematical reasons nad arguments that could convince a friend that log (M+N) = logM + log N
What misconceptions might these two problems present for students? Why is it important to address misconceptions early?
How would you respond to a student who sees little or no meaning in solving either problems?
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Logarithmic Misconceptions
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Logarithmic Misconceptions
52x = 53x + 2 This exponential equation has a negative solution.
Simplifying
52x = 53x + 2
2x = 3x+2
Combine the like terms;
2x -3x = 2 +3x-3x;
-x = 2
Divide each side by '-1'.
x =- 2
We can graph the logarithmic function without starting with the exponential. For example, when we want to draw the graph of y=Log2(x), we begin by finding the values of y because, for x values, we will choose at least 3 numbers from the x-axis, like 0,1,2. Then we substitute in the equation to find the values for y.
x
(y) = Log2(x)
0
0
1
0
2
1
Then draw the graph for these values.
Log (M+N) =LogM + LogN; this can be proved by using simple mathematical concepts of opening the ...
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