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2 years ago

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]2 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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1 year ago

827 divided by 1120

KiRa [710]

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3 years ago

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A professor's son, having made the wise decision to drop out of college, has been finding his way in life taking one job or anot

Trava [24]

Answer:

88.88% probability that it endures for less than a year and a half

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

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