# Nail Length

Discussion in 'Other Pre-University Math' started by nycmathguy, Oct 20, 2021.

1. ### nycmathguy

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Section 3.3
Question 88

Note: I am using Example 7 as a guide for me to work out 88.

I have to use the given information in the box above to find at least one point in the form
(ln x, ln y).

I will use x = 2, y = 0.113.

So, (ln 2, ln 0.113) becomes (0.693, -2.180).

I now must find the slope m using (0.693, -2.180) and the origin.

m = (-2.180 - 0)/(0.693 - 0)

m = -2.180/0.693

m = -3.1457431457

Rounding to two decimal places, I get m = -3.15.

I know use the point-slope formula.

y - y_1 = m(x - x_1)

I will use the point (0, 0).

y - 0 = -3.15(x - 0)

y = -3.15x

I say the logarithmic equation is y = -3.15 ln x.

You say?

nycmathguy, Oct 20, 2021

2. ### MathLover1

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why did you choose (0,0) as a second point?

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MathLover1, Oct 20, 2021
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3. ### nycmathguy

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I selected (0, 0) following Example 7. If wrong, which two points should I have chosen?

nycmathguy, Oct 20, 2021
4. ### MathLover1

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ok

MathLover1, Oct 20, 2021
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5. ### nycmathguy

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Is my equation right or wrong?

nycmathguy, Oct 21, 2021
6. ### MathLover1

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in Example 7 ,
if x=1 and y=1 (from given table) then (ln(x), ln(y)) =(ln(1), ln(1)) =(0, 0)
if x=1.524 and y=1.881 (from given table) then (ln(x), ln(y)) =(ln(1.524), ln(1.881)) =(0.421, 0.632)
then was calculated slope

since fig. 3.14 cannot be used for 88, and you have to use two of given points from the table

MathLover1, Oct 21, 2021
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