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Alex787 [66]
3 years ago
10

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variab

les represent positive real numbers. (2 points) 4log x + 3log y
Mathematics
1 answer:
vladimir1956 [14]3 years ago
7 0

4log(x) x + 3log(y)


The power rule of logarithms states:

log(4)^X = Xlog(4)


The product rule of logarithms states:

log(x) + log(y) = log(xy)


Rewrite each logarithm using the power rule of logarithms:

4log(x) = log(x)^4

3log(y) = log(y)^3


log(x)^4 + log(y)^3


Combine them using the product rule of logarithms:

log(x)^4 + log(y)^3 = log(x^4y^3)


Answer:

log(x^4y^3)

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Park two has 12 more benches than Park one. If 2 benches were transferred from Park two to Park one, then Park two would have 2
marta [7]

Answer:

There were 6 benches in park 1 and 18 benches in park 2.

Step-by-step explanation:

Let x be the no of benches in Park 1 and y in park 2.

Given that there are 12 more benches in park 2 than 1

Writing this in equation form, we have y = x+12 ... i

Next is if 2 benches were transferred from park 2 to park 1, then we have

x+2 in park 1 and y-2 in park 2.

Given that y-2 = twice that of x+2

Or y-2 = 2x+4 ... ii

Rewrite by adding 2 to both sides of equation ii.

y = 2x+6 ... iii

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Or x =6

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Verify:

Original benches 6 and 18.

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6 0
2 years ago
Read 2 more answers
The width of a rectangle is the sum of the length and 1. The area of the rectangle is 20 units. What is the width, in units, of
IRISSAK [1]

Answer:

W=5

Step-by-step explanation:

W=Width=Length + 1

L = Length

Area = Length * Width = 20

Area = L * W = L * (L+1) = 20

Distribute the L:   L^2 + L = 20

Subtract 20 from both sides: L^2 + L -20 = 20-20

Simplify:  L^2+L-20=0

Factor (L-4)(L+5)=0

Solve using the zero property: L-4=0, L=4      L+5=0, L=-5

The two options for length are 4 and -5. Only 4 will work for L since it cannot be negative.   Width is Length + 1 = 5

6 0
3 years ago
If f (x) = StartRoot x EndRoot + 12 and g (x) = 2 StartRoot x EndRoot, what is the value of (f – g)(144)
Luda [366]

The value of (f-g)(144) is 0

Step-by-step explanation:

We are given:

f(x)=\sqrt{x}+12\,\,and\,\,\\ g(x)=2\sqrt{x}

We need to find value of (f-g)(144)

We will put x=144 for both f(x) and g(x)

(f-g)(144)=f(144)-g(144)\\=\sqrt{144}+12-(2\sqrt{12})\\=12+12-(2(12)\\=24-24\\=0

So, the value of (f-g)(144) is 0

Keywords: Composite Functions

Learn more about Composite Functions at:

  • brainly.com/question/4939434
  • brainly.com/question/2723982
  • brainly.com/question/10772025

#learnwithBrainly

4 0
3 years ago
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