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jek_recluse
2 months ago
5

Explain the error in the solution below. What additional step needs to be completed? log x – log53 = 2log53 log x = 3log53 log x

= log533 x = 27
Mathematics
2 answers:
PIT_PIT [12.4K]2 months ago
5 0
The mistake lies in the fact that the logarithms have different bases. The one-to-one property of logarithms cannot be applied unless the bases are identical. <span>To correct this, the change of base formula should be used to express the logarithms with a uniform base.
I have confirmed this using Edge.</span>
tester [12.3K]2 months ago
5 0

Answer:

The error occurs at step 3,

Steps 4 through 9 provide the proper correction.

Detailed explanation:

Given the solution below,

\log x -\log_5 3 = 2\log_5 3\\\log x = 3\log_5 3\\\log x = \log_5 33\\x = 27

Task: Identify the error and determine the necessary additional step.

Solution: The fault is in step 3 and a further step must be inserted afterwards.

We proceed as follows:

Step 1 - \log x -\log_5 3 = 2\log_5 3

Step 2 - \log x = 3\log_5 3

Step 3 - \log x =\log_5 3^3

Step 4 - \log x=\log_5 27

By applying the change of base rule for logarithms,

\log_b a=\frac{\log a}{\log b}

Step 5 - \log x=\frac{\log 27}{\log 5}

Step 6 - \log x=\frac{1.431}{0.698}

Step 7 - \log x=2.050

Step 8 - x=10^{2.050}

Step 9 - x=112.20

The steps from 4 to 9 represent the correct procedure.

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If m&lt;9=97° and m&lt;12=114°, find each measure. I have to show my work.
Leona [12618]

Solution/Step-by-step breakdown:

Information provided:

m<9 = 97°

m<12 = 114°

a. m<1 = m<9 because they are corresponding angles, which are equal.

m<1 = 97° (using substitution)

b. m<2 + m<1 = 180° (since they form a linear pair)

m<2 + 97° = 180° (substitute the value)

m<2 = 180 - 97 (subtracting 97 from both sides)

m<2 = 83°

c. m<3 = m<11 (as they are corresponding angles)

m<11 + m<12 = 180° (linear pair)

m<11 + 114° = 180° (substituting the known angle)

m<11 = 180 - 114

m<11 = 66°

m<3 = m<11 = 66°

d. m<4 + m<3 = 180° (linear pair)

m<4 + 66° = 180° (substituting the known angle)

m<4 = 180 - 66

m<4 = 114°

e. m<5 = m<2 as vertical angles are equal.

m<5 = 83° (using substitution)

f. m<6 = m<1 (vertical angles are equal)

m<6 = 97° (using substitution)

g. m<7 = m<4 (as vertical angles are equal)

m<7 = 114° (using substitution)

h. m<8 = m<3 (due to vertical angles being equal)

m<8 = 66° (using substitution)

i. m<10 = m<2 (corresponding angles are equal)

m<10 = 83° (using substitution)

j. m<11 = m<3 (because they are vertical angles)

m<11 = 66° (using substitution)

k. m<13 = m<5 (corresponding angles)

m<13 = 83° (applying substitution)

l. m<14 = m<9 (as vertical angles)

m<14 = 97° (applying substitution)

m. m<15 = m<12 (as vertical angles)

m<15 = 114° (applying substitution)

n. m<16 = m<11 (because they are vertical angles)

m<16 = 66° (applying substitution)

3 0
1 month ago
Five more than twice a number is three times the difference of that number and two. What is the number.
Zina [12379]

Response:

2(3-n)+5.

Clarification:

Twice a number plus five equals three times the difference between that number and two. "More" indicates addition, hence twice the number is represented as multiplying N (or whatever variable) with the determination that it equals three times the reduction of that number and two.

5 0
1 month ago
Chris buys 8 more Ninja Turtles than Star Wars action figures. The Ninja Turtles cost $7 each and the Star Wars cost $9 each. Wr
Svet_ta [12734]
Total Cost, C = $(16S + 56). Step-by-step explanation: Chris purchases 8 more Ninja Turtles than Star Wars action figures. The cost per Ninja Turtle is $7, while each Star Wars figure costs $9. If we let S represent the number of Star Wars figures bought, then the number of Ninja Turtles becomes S + 8. The cost for S Star Wars figures is $9S. Similarly, for (S + 8) Ninja Turtles, the total cost is $(7S + 56). Therefore, the overall Total Cost is represented by the sum of the costs for both types of figures, leading to the Total Cost being expressed as C = 9S + (7S + 56).
4 0
13 days ago
1. The C major key, starting with the middle C, consists of seven notes (white keys on the piano) with the following frequencies
Zina [12379]
1.) <span>The ratio of note A compared to middle C is 440.0 / 261.6 = 1.6820 ≈ 1.6818

2.) </span><span>The D note's ratio against middle C is 293.7 / 261.6 = 1.1227

3.) </span><span>D# = 293.6 multiplied by 1.0595 equals 311.1

4.) </span><span>The frequency ratio of G compared to C is 1: 262/392 = 1: 0.6683 ≈ 3: 2

5.) </span><span>The frequency ratio of E to C is 1: 262/330 = 1: 0.7939 ≈ 5: 4

6.) The </span><span>element in a musical note referred to as pitch is the frequency.</span>
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1 month ago
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What is the slope of 1.5x+4.5y=18
Inessa [12570]
The x intercept is at (12,0). To find it, start with the equation 1.5x + 4.5y = 18, and subtract 1.5x from both sides. This gives you 4.5y = -1.5x + 18. Next, divide everything by 4.5, resulting in y = -1/3x + 4. Hence, the slope of the line is -1/3, and the y intercept is at (0,4). To determine the x intercept, set y to 0. Plugging this into the equation yields: 1.5x + 4.5(0) = 18, simplifying to 1.5x = 18. Dividing both sides by 1.5 gives x = 12.
5 0
12 days ago
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