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Vadim26 [7]
2 years ago
5

Solve log base 6 (x-6) - log base 6 (x + 4) = 2

Mathematics
1 answer:
Ray Of Light [21]2 years ago
4 0

Answer:

no solutions

Step-by-step explanation:

Since the two terms have the same base, we are able to use the rule for subtracting logarithms:

log_{b}(x) - log_{b}(y) = log_{b}(\frac{x}{y} )

Therefore, the equation can be written as:

log_{6}(\frac{x-6}{x+4} )=2

By using the definition of a logarithm we can say that:

\frac{x-6}{x+4} = 6^{2}\\\frac{x-6}{x+4} = 36\\x -6 = 36x+144\\35x = -150\\x =-\frac{30}{7}

When plugging this solution in, you find that the term log_{6}(x-6) has x-6 evaluate to a number less than 0. This is not included in the domain of log functions, so -\frac{30}{7} is not a valid solution. This means that there are no solutions.

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Step-by-step explanation:

m=7 makes the equation true

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marysya [2.9K]
First, subtract to get the difference.
2.85 – 2.78 = 0.07

Next, divide 2.78 by 100
2.78 ÷ 100 = 0.0278
So, 0.0278 is 1%. Divide 0.07 by 0.0278 to get the answer.
0.07 ÷ 0.0278 ≈ 2.518
2.518 ≈2.5
Therefore, the percentage increase is approximately 2.5% (that's the answer).

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8 0
3 years ago
Time to paint the living room. The room measures 20 feet wide by 30 feet long by 12
chubhunter [2.5K]

The cost to paint the walls and the ceiling is $855

<h3></h3><h3>How much will it cost?</h3>

First, we need to find the area that will be painted.

The area of two of the walls is:

A = 20ft*12ft = 240ft²

The area of the other two walls:

A' = 30ft*12ft = 360ft²

The area of the ceiling is:

A'' = 20ft*30ft = 600ft²

We also need to subtract the areas of the two doors and the 4 windows.

Each door is 7ft by 3ft, so the area of each door is:

a = 7ft*3ft = 21ft²

Each window is 4ft by 3ft:

a' = 4ft*3ft = 12ft²

Then the total area that will be painted is:

area = 2A + 2A' + A - 2a - 4a'

area = 2*( 240ft²) + 2*(360ft²) + 600ft² - 2*(21ft²) - 4*(12ft²)

area = 1,710 ft²

We know that we need two coats of paint to cover that area, and the cost per square foot of paint is $0.25, then the total cost is:

C = $0.25*2*(1,710) = $855

The cost to paint the walls and the ceiling is $855

If you want to learn more about areas:

brainly.com/question/24487155

#SPJ1

6 0
2 years ago
Ryan took out a 66 month loan to pay for a 28500 car.if he paid 33829.50,in total at the end of the loan,find the interest rate
professor190 [17]

9514 1404 393

Answer:

  3.4%

Step-by-step explanation:

The total amount due is ...

  A = P(1 +rt/12) . . . . . principal P, annual rate r, t months

  33829.50 = 28500(1 +66/12r)

  1.187 = 1 +5.5r . . . . . divide by 28500, simplify

  0.185/5.5 = r = 0.034 = 3.4%

The interest rate on the loan is 3.4%.

3 0
3 years ago
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