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3 years ago

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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The amount ofmoney is in the ratio 8:3 if the first amount is 9.92 what is the second amount?

BARSIC [14]

Answer:

The second amount is 3.72

Step-by-step explanation:

Given

$First : Second = 8 : 3$

$First = 9.92$

Required

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$First : Second = 8 : 3$

Substitute 9.92 for First

$9.92: Second = 8 : 3$

Express as fraction

$\frac{Second}{9.92} = \frac{3}{8}$

Multiply both sides by 9.92

$9.92 * \frac{Second}{9.92} = \frac{3}{8}*9.92$

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3 years ago

For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so:

$\theta\neq \pi$

having said this, we can now start solving the equation:

$tan(\frac{\theta}{2})=sin(\theta)$

we can start solving this equation by using the half angle formula, such a formula tells us the following:

$tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}$

so we can substitute it into our equation:

$\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)$

we can now multiply both sides of the equation by $sin(\theta)$

so we get:

$1-cos(\theta)=sin^{2}(\theta)$

we can use the pythagorean identity to rewrite $sin^{2}(\theta)$ in terms of cos:

$sin^{2}(\theta)=1-cos^{2}(\theta)$

so we get:

$1-cos(\theta)=1-cos^{2}(\theta)$

we can subtract a 1 from both sides of the equation so we end up with:

$-cos(\theta)=-cos^{2}(\theta)$

and we can now add $cos^{2}(\theta)$

to both sides of the equation so we get:

$cos^{2}(\theta)-cos(\theta)=0$

and we can solve this equation by factoring. We can factor $cos(\theta)$ to get:

$cos(\theta)(cos(\theta)-1)=0$

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

$cos(\theta)=0$

$\theta=cos^{-1}(0)$

$\theta={\frac{\pi}{2}, \frac{3\pi}{2}}$

Equation 2:

$cos(\theta)-1=0$

we add a 1 to both sides of the equation so we get:

$cos(\theta)=1$

$\theta=cos^{-1}(1)$

$\theta=0$

so we end up with three answers to this equation:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

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2 years ago

HELPP MEE PLEASEEEEEE

Rudiy27

Answer:

wouldn't it be 5m....??

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The area and perimeter of the lawn will be 322 square feet and 74 feet. If the lawn will be mowed. Then the area will be used. If the lawn will be surrounded by a rope. Then the perimeter will be used.

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The figure below shows a rectangular lawn.

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More about the rectangle link is given below.

brainly.com/question/10046743

#SPJ1

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2 years ago