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SVEN [57.7K]
3 years ago
10

Rewrite the following expression as a single logarithm. Which letter is the correct answer?

Mathematics
2 answers:
Pepsi [2]3 years ago
8 0

Answer: OPTION B

Step-by-step explanation:

You need to remember the logarithms properties:

log(a)+log(b)=log(ab)\\\\log(a)-log(b)=log(\frac{a}{b})\\\\log(a)^b=blog(a)

Then, you can rewrite the expression as a single logarithm:

log(x+3)^2+log(x-7)^3-log(x-2)^5-log(x^2)\\\\log((x+3)^2(x-7)^3)-log(\frac{(x-2)}{(x^2)})\\\\log(\frac{(x+3)^2(x-7)^3}{x^2(x-2)^5})

This matches with the option B.

Ne4ueva [31]3 years ago
3 0

Answer:

The single logarithm is ㏒[(x + 3)²(x - 7)³/(x²)(x - 2)^5] ⇒ answer B

Step-by-step explanation:

* Lets revise the rule of the logarithmic functions

# ㏒ a + ㏒ b = ㏒ ab

# ㏒ a - ㏒ b = ㏒ a/b

# ㏒ a^n = n ㏒ a

# ㏒ 1 = 0

* Now lets solve the problem

∵ 2㏒(x + 3) + 3㏒(x - 7) - 5㏒(x - 2) - ㏒(x²)

- To make this expression as a single logarithm, change the plus

  to multiplication and minus to division

# 2㏒(x + 3) = ㏒(x + 3)² ⇒ using the third rule up

# 3㏒(x - 7) = ㏒(x - 7)³ ⇒ using the third rule up

# 5㏒(x - 2) = ㏒(x - 2)^5 ⇒ using the third rule up

* lets write the expression

∴ ㏒(x + 3)² + ㏒(x - 7)³- ㏒(x - 2)^5 - log(x²)

# ㏒(x + 3)² + ㏒(x - 7)³  ⇒ change them to single logarithm

∴  ㏒(x + 3)² + ㏒(x - 7)³ = ㏒(x + 3)²(x - 7)³

# - ㏒(x - 2)^5 - log(x²) ⇒ take (-) as a common factor

∴ - (㏒(x - 2)^5 + log(x²)) = - ㏒(x²)(x - 2)^5

∴ ㏒(x + 3)² + ㏒(x - 7)³- ㏒(x - 2)^5 - log(x²) =

  ㏒(x + 3)²(x - 7)³ - ㏒(x²)(x - 2)^5

* Change ㏒(x + 3)²(x - 7)³ - ㏒(x²)(x - 2)^5 to a single logarithm

∴ ㏒(x + 3)²(x - 7)³ - ㏒(x²)(x - 2)^5 = ㏒[(x + 3)²(x - 7)³/(x²)(x - 2)^5]

* The single logarithm is ㏒[(x + 3)²(x - 7)³/(x²)(x - 2)^5]

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Step-by-step explanation:

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The slope, y-intercept and equation of the function.

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Take any two points on the table.

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3 years ago
What is the range of the function in the graph?
Verdich [7]

The range of the function in the graph given can be expressed as: D. 20 ≤ s ≤ 100.

<h3>What is the Range and Domain of a Function?</h3>

All the possible set of x-values that are plotted on the horizontal axis (x-axis) are the domain of a function. In order words, they are the inputs of the function.

On the other hand, all the corresponding set of x-values that are plotted on the vertical axis (y-axis) are the range of a function. In order words, they are the outputs of the function.

In the graph given below that shows a function, s is plotted on the vertical axis (y-axis), and its values starts from 20, up to 100. The range can be said to be all values of s that are from 20 to 100.

Therefore, the range of the function in the graph given can be expressed as: D. 20 ≤ s ≤ 100.

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What is the solution to the equation below? Round your answer to two decimal places? (apex) 5+8*In x=15.8
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Option A : $x=3.86$ is the solution of the equation.

Explanation:

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To determine the value of x, let us simplify the equation.

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Simplifying, we get,

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0.285714285 nearest thousandth​
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Answer:

0.286

Hope that helps!

Step-by-step explanation:

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