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Fiesta28 [93]
3 years ago
11

expression to approximate log a of x for all positive numbers a, b, and x, where a is not equal to 1 and b is not equal to one

Mathematics
1 answer:
amid [387]3 years ago
7 0

Question:

Approximate log base b of x, log_b(x).

Of course x can't be negative, and b > 1.


Answer:

f(x) = (-1/x + 1) / (-1/b + 1)


Step-by-step explanation:

log(1) is zero for any base.

log is strictly increasing.

log_b(b) = 1

As x descends to zero, log(x) diverges to -infinity


Graph of f(x) = (-1/x + 1)/a is reminiscent of log(x), with f(1) = 0.


Find a such that f(b) = 1

1 = f(b) = (-1/b + 1)/a

a = (-1/b + 1)


Substitute for a:

f(x) = (-1/x + 1) / (-1/b + 1)

f(1) = 0

f(b) = (-1/b + 1) / (-1/b + 1) = 1




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\begin{gathered} (x_1,y_1)=(4,2) \\ (x_2,y_2)=(7,6.5) \end{gathered}

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\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{6.5-2}{7-4} \end{gathered}

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The slope is 1.5.

The formula of (10, 8) anjd (-5,8) is

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Answer: \bold{\sqrt{74}}

<u>Step-by-step explanation:</u>

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The coordinate plane below represents a city. Points A through F are schools in the city.
astra-53 [7]
Part A:
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Part B:
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WITCHER [35]
<h2><u>Answer</u>:</h2>

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<h2><u>Step-by-step explanation</u>:</h2>

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Hence answer is 81.

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