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Anna [14]
3 years ago
6

The table shows a student's proof of the quotient rule for logarithms.

Mathematics
1 answer:
nikklg [1K]3 years ago
5 0

Answer:

The error is at step (3) .

The correct step (3) will be,

\log_{b}(\frac {b^{x}}{b^{y}})

= \log_{b}(b^{x - y})   [by using the laws of indices]

All other steps are correct.

Step-by-step explanation:

The error is at the step (3) , because the student has tried to prove the quotient rule of logarithms by using the property i.e., 'The quotient rule of logarithm' itself , i.e. ,by  assuming the property does hold before proving it. So, the proof is fallacious.

The correct step (3) will be,

\log_{b}(\frac {b^{x}}{b^{y}})

= \log_{b}(b^{x - y})   [by using the laws of indices]

All other steps are correct.

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Any help is appreciated because I have a probe in a couple of hours
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1+1/x^2 when multiplied by x^2 we get: (x^2+1)/x^2.

5 0
3 years ago
Given m∠B = 62, m∠C = 54 and line AD bisects ∠BAC, find m∠ADB
insens350 [35]
THE ANSWER IS: 86 degrees

first find the measure of angle a: since all angles of a triangle add up to 180, add the measures of angle b and angle c then subtract it from 180 to get angle a: 62+54=116, 180-116=64

since we know line AD bisects angle a, we can divide 64 degrees by 2 to find angle BAD: which is 32 degrees

then subtract both 62 and 32 from 180 to get 86 degrees for angle ADB

8 0
3 years ago
In the figure below mPUR =77 and mST=74 Find mPR
eduard

Answer:

a)

<u>The angle formed by intersecting chords is half of the sum of the intercepted arcs:</u>

  • 1/2(mST + mPR) = m∠PUR
  • 1.2(74° + mPR) = 77°
  • 74° + mPR = 2*77°
  • mPR = 154° - 74°
  • mPR = 80°

b)

<u>The angle formed by two tangents is the half of the difference of the intercepted arcs:</u>

  • m∠PSR = 1/2(mPTR - mPR)
  • m∠PSR = 1/2(247° - (360° - 247°))
  • m∠PSR = 247° - 180°
  • m∠PSR = 67°
8 0
3 years ago
What is <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D5%20x%20%5Cfrac%7B1%7D%7B3%7D" id="TexFormula1" title="\frac{1}{3
mr_godi [17]

Answer:

1.77777778

Step-by-step explanation:


5 0
3 years ago
Seven less than the product of a number n and 1/6 is no more than 94
antiseptic1488 [7]

Answer:

  • n ≤ 606

Step-by-step explanation:

<u>Seven less than the product of a number n and 1/6 is no more than 94, translating:</u>

  • n*1/6 - 7 ≤ 94

<u>Solving for n:</u>

  • n/6  ≤ 94 + 7
  • n/6 ≤ 101
  • n ≤ 101*6
  • n ≤ 606
4 0
3 years ago
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