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3 years ago

7

Expanding logarithmic Expression In Exercise,Use the properties of logarithms to rewrite the expression as a sum,difference,or m

ultipal of logarithms.See example 3.
In 3x(x + 1)/(2x + 1)^2

1 answer:

Liono4ka [1.6K]3 years ago

6 0

Answer:

$\ln{(3x)}+\ln{(x+1)}-2\ln{(2x+1)}$

Step-by-step explanation:

we need to keep in mind two properties of log:

$\ln{ab}=\ln{a}+\ln{b}$

$\ln{\dfrac{a}{b}}=\ln{a}-\ln{b}$
$\ln{a^b}=b\ln{a}$

$\ln{\dfrac{3x(x+1)}{(2x+1)^2}}$

$\ln{\left(\dfrac{3x(x+1)}{(2x+1)^2}\right)}\\\ln{(3x(x+1))}-\ln{((2x+1)^2)}\\\ln{(3x)}+\ln{(x+1)}-\ln{((2x+1)^2)}$

$\ln{(3x)}+\ln{(x+1)}-2\ln{(2x+1)}$

this is the rewritten expression!

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Given right triangle ABC, what is the value of tan(A)? Five-thirteenths Twelve-thirteenths Twelve-fifths Thirteen-twelfths

WITCHER [35]

Answer:

Twelve-fifths.

Step-by-step explanation:

The diagram is shown below

Given triangle be right angled at $B$ ,

Withe reference to $\angle A$ ,

Its opposite side is $BC=12$ , adjacent side is $AB=5$ and hypotenuse is $AC=13$

We are to find the value of $tan(A)$

We know $tan=\frac{opposite}{adjacent}$

Substituting the above values we get,

$tan(A)= \frac{BC}{AB}=\frac{12}{5}$

So the answer is Twelve-fifths.

8 0

3 years ago

Read 2 more answers

Brenda has a job offers at two companies. One company offers a starting salary of $75,000 with a raise of $2,500 each year. The

Sedbober [7]

For this case, the first thing we must do is define variables.

We have then:

x: number of years

y: total salary

For company 1 we have:

$y = 2500x + 75000$

For company 2 we have:

$y = 5000x + 55000$

By the time both salaries are equal we have:

$2500x + 75000 = 5000x + 55000$

From here, we clear the value of x.

We have then:

$5000x - 2500x = 75000 - 55000\\2500x = 20000$

$x = \frac{20000}{2500}\\x = 8$

Answer:

Brenda's salary would be the same with both companies in 8 years.

4 0

3 years ago

Find the midpoint of the segment with the given endpoints (8, -7) and (-9,8)

Svet_ta [14]

Answer:

$\displaystyle (\frac{-1}{2},\frac{1}{2})$

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

<u>Algebra I</u>

Coordinate Planes

Coordinates (x, y)

Midpoint Formula: $\displaystyle (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

Point (8, -7)

Point (-9, 8)

<u>Step 2: Find Midpoint</u>

Substitute in points [Midpoint Formula]: $\displaystyle (\frac{8 - 9}{2},\frac{-7 + 8}{2})$
[Order of Operations] Evaluate: $\displaystyle (\frac{-1}{2},\frac{1}{2})$

6 0

3 years ago

Estimate the perimeter and area of the shaded figure to the nearest tenth.

Maru [420]

Answer:

Perimeter = 18.7 units

Area = 13.5 units²

Step-by-step explanation:

Perimeter of ADEC = AD + DE + EC + AC

Length of AD = 3 units

By applying Pythagoras theorem in ΔDBE,

DE² = DB² + BE²

DE² = 3² + 3²

DE = √18

DE = 4.24 units

Length of EC = 3 units

By applying Pythagoras theorem in ΔABC,

AC² = AB² + BC²

AC² = 6² + 6²

AC = √72

AC = 8.49 units

Perimeter of ADEC = 3 + 4.24 + 3 + 8.49

= 18.73 units

≈ 18.7 units

Area of ADEC = Area of ΔABC - Area of ΔBDE

Area of ΔABC = $\frac{1}{2}(AB)(BC)$

= $\frac{1}{2}(6)(6)$

= 18 units²

Area of ΔBDE = $\frac{1}{2}(BD)(BE)$

= $\frac{1}{2}(3)(3)$

= 4.5 units²

Area of ADEC = 18 - 4.5

= 13.5 units²

6 0

3 years ago

What is the value of n so that the expression x^2 + 11x + n is a perfect trinomial?

lora16 [44]

The answer is c) 30.25

6 0

4 years ago