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2 months ago

Guest #3634

2 months ago

Given:

4log1/2^w (2log1/2^u-3log1/2^v)

Req'd:

Single logarithm = ?

Sol'n:

First remove the parenthesis,

4 log 1/2 (w) + 2 log 1/2 (u) - 3 log 1/2 (v)

Simplify each term,

Simplify the 4 log 1/2 (w) by moving the constant 4 inside the logarithm;

Simplify the 2 log 1/2 (u) by moving the constant 2 inside the logarithm;

Simplify the -3 log 1/2 (v) by moving the constant -3 inside the logarithm:

log 1/2 (w^4) + 2 log 1/2 (u) - 3 log 1/2 (v)

log 1/2 (w^4) + log 1/2 (u^2) - log 1/2 (v^3)

We have to use the product property of logarithms which is log of b (x) + log of b (y) = log of b (xy):

Thus,

Log of 1/2 (w^4 u^2) - log of 1/2 (v^3)

then use the quotient property of logarithms which is log of b (x) - log of b (y) = log of b (x/y)

Therefore,

log of 1/2 (w^4 u^2 / v^3)

and for the final step and answer, reorder or rearrange w^4 and u^2:

**log of 1/2 (u^2 w^4 / v^3) **

4log1/2^w (2log1/2^u-3log1/2^v)

Req'd:

Single logarithm = ?

Sol'n:

First remove the parenthesis,

4 log 1/2 (w) + 2 log 1/2 (u) - 3 log 1/2 (v)

Simplify each term,

Simplify the 4 log 1/2 (w) by moving the constant 4 inside the logarithm;

Simplify the 2 log 1/2 (u) by moving the constant 2 inside the logarithm;

Simplify the -3 log 1/2 (v) by moving the constant -3 inside the logarithm:

log 1/2 (w^4) + 2 log 1/2 (u) - 3 log 1/2 (v)

log 1/2 (w^4) + log 1/2 (u^2) - log 1/2 (v^3)

We have to use the product property of logarithms which is log of b (x) + log of b (y) = log of b (xy):

Thus,

Log of 1/2 (w^4 u^2) - log of 1/2 (v^3)

then use the quotient property of logarithms which is log of b (x) - log of b (y) = log of b (x/y)

Therefore,

log of 1/2 (w^4 u^2 / v^3)

and for the final step and answer, reorder or rearrange w^4 and u^2:

Guest #3635

2 months ago

**Answer:**

**Step-by-step explanation:**

**Given :** Expression

**To write : **As a single logarithm?

**Solution :**

**Remove parenthesis,**

**Simplify each term by applying logarithmic property,**

**Use the product property of logarithms,**

**Use the quotient property of logarithms,**

**Therefore, **

Question

Change 5/8 to a percentage.
A. 87.5%
B. 62.5%
C. 92.5%
D. 37.5%

Solution 1

5/8 = 5 ÷ 8 = .625

move decimal 2 places to right for %

.625 = 62.5%

move decimal 2 places to right for %

.625 = 62.5%

Question

The height reached by amal's rocket was 1/4 of the height reached by min's rocket. Amal's rocket REAched a height of 15 meters. Which equation could be used to find the height reached by min's rocket

Solution 1

To solve this problem you must keep on min the information given in the problem shown above:

1- You have that

- The height reached by amal's rocket was 1/4 of the height reached by min's rocket.

- Amal's rocket REAched a height of 15 meters.

2. Therefore, let's call "x" to the height reached by min's rocket. Then, you have:

(1/4)x=15

x/4=15

Which equation could be used to find the height reached by min's rocket?

** The answer is: x/4=15**

1- You have that

- The height reached by amal's rocket was 1/4 of the height reached by min's rocket.

- Amal's rocket REAched a height of 15 meters.

2. Therefore, let's call "x" to the height reached by min's rocket. Then, you have:

(1/4)x=15

x/4=15

Which equation could be used to find the height reached by min's rocket?

Question

Marina correctly simplified the expression (-4a^-2 b^4)/(8a^-6b^-3) assuming that a does not equal 0 and b does not equal 0. Her simplified expression is below. -1/2a^4b^
The exponent of the variable b in Marina’s solution should be...

Solution 1

For this case we have the following expression:

(-4a ^ -2 b ^ 4) / (8a ^ -6b ^ -3)

We can rewrite the expression using properties of exponents.

We have then:

(-4/8) * ((a ^ (- 2 - (- 6))) (b ^ (4 - (- 3))))

Rewriting we have:

(-2/4) * ((a ^ (- 2 + 6)) (b ^ (4 + 3)))

(-1/2) * ((a ^ 4) (b ^ 7))

-1 / 2a ^ 4b ^ 7

**Answer:**

**The exponent of the variable b in Marina's solution should be 7**

(-4a ^ -2 b ^ 4) / (8a ^ -6b ^ -3)

We can rewrite the expression using properties of exponents.

We have then:

(-4/8) * ((a ^ (- 2 - (- 6))) (b ^ (4 - (- 3))))

Rewriting we have:

(-2/4) * ((a ^ (- 2 + 6)) (b ^ (4 + 3)))

(-1/2) * ((a ^ 4) (b ^ 7))

-1 / 2a ^ 4b ^ 7

Solution 2

**Answer:**

7 is correct!

**Step-by-step explanation:**

hope that this helps. Peace and Love

Question

Fórmula para sacar el área de un circulo

Solution 1

Fórmula para sacar el área de un circulo:

Question

Which of the following pairs of numbers contain like fractions? A. 3
/2
and 2
/3
B. 6
/7
and 15
/7
C. 5
/6
and 10/12
D. 31
/2
and 43
/4

Solution 1

C. 5/6 and 10/12

If you simplify 10/12 but the greatest common factor of 10 and 12, which is 2, you get the answer of 5/6. Now if you multiple 5/6 by two, you get 10/12. Either way, both fractions are clearly equivalent.

If you simplify 10/12 but the greatest common factor of 10 and 12, which is 2, you get the answer of 5/6. Now if you multiple 5/6 by two, you get 10/12. Either way, both fractions are clearly equivalent.

Question

A teacher asked her students to divide a large number by 50. • Aslan divided the number by 50.
• Lucy divided the number by 5 and then divided the answer she got by 10.
• Jack divided the number by 10 and then divided the answer he got by 40.
Who among these got the correct answer assuming they did NOT make mistakes in division?

Solution 1

**Answer:**

c

**Step-by-step explanation:**

Question

WHAT IS THE DEFINITION OF INDEMNITY

Solution 1

Indemnity: Security or protection against a loss or other financial burden

Question

Find the sum of (3x^2+16x+9) and (-16x-12)

Solution 1

Remove the brackets:

Combine like terms:

Take out common factor 3:

Factorise (x² - 1):

Question

The football team is running a jackpot in which the prize will start at $2500 for the first game, and then increase $500 each game if there is no winner. If there are no winners, find the value of the jackpot at the end of their 16-game season.

Solution 1

The **value** of the **jackpot** at the end of the **16-game** season will be $10,000.

An **expression** contains one or more **terms** with addition, subtraction, multiplication, and division.

We always combine the **like** **terms** in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The **jackpot** **prize** starts at $2500 for the first game and **increases** by $500 for each game if there is no winner.

For the **second** **game**,

The prize will be $2500 + $500 = $3000.

For the **third** **game**,

The prize will be $3000 + $500 = $3500.

**Continuing** in this pattern, the prize for the 16th game will be:

$2500 + ($500 × 15)

= $2500 + $7500

= $10000

Therefore,

The **value** of the **jackpot** at the end of the **16-game** season will be $10,000.

Learn more about **expressions** here:

#SPJ3

Solution 2

10,500 because if you first add 2500 and 500 its already 1 so fifteen times mor and thats 10,500

Question

Ms. Bergstedt asked two students to come up with two different sequences. Jay created this sequence: The first term is 4 and each term after the first is 6 more than the preceding term. Joe created this sequence: The first term is 8 and each term after the first term is 5 more than the preceding term. What is the value of the first term that they have in common?

Solution 1

Well, create an equation.

y=6x+4 and y=5x+8

From there you would go to Desmos.com and find out. The answer is 4,28.

This means it's the fourth term and the number is 28.

y=6x+4 and y=5x+8

From there you would go to Desmos.com and find out. The answer is 4,28.

This means it's the fourth term and the number is 28.

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