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3 years ago

Simplify log (x2-y2)- log (x-y)=

2 answers:

8 0

Using the law of logarithm. LogA - LogB = Log(A/B)

log(x²-y²) - log(x-y) = log((x²-y²)/(x-y))

Note by difference of two squares, (x²-y²) = (x-y)(x+y)

Simplifying (x²-y²)/(x-y) = (x-y)(x+y)/(x-y) = (x+y)

Therefore log(x²-y²) - log(x-y) = log((x²-y²)/(x-y)) = log((x-y)(x+y)/(x-y)) = log(x+y)

jok3333 [9.3K]3 years ago

3 0

Remember:
log A - log B=log (A/B)
(a²-b²)=(a+b)(a-b).

Therefore

log (x²-y²)-log(x-y)=log[(x²-y²)/(x-y)]= log[(x+y)(x-y) / (x-y)]=log (x+y)

Answer: log (x²-y²)-log(x-y)=log (x+y)

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A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is la

Minchanka [31]

The exponential function which represented by the values in the table is $f(x)=4(\frac{1}{2})^{x}$ ⇒ 3rd answer

Step-by-step explanation:

The form of the exponential function is $f(x)=a(b)^{x}$ , where

a is the initial value (when x = 0)
b is the growth/decay factor
If k > 1, then it is a growth factor
If 0 < k < 1, then it is a decay factor

The table:

→ x : f(x)

→ -2 : 16

→ -1 : 8

→ 0 : 4

→ 1 : 2

→ 2 : 1

∵ $f(x)=a(b)^{x}$

- To find the exponential function substitute the value of x and f(x)

by some values from the table to find a and b, at first use the

point (0 , 4) to find the value of a

∵ x = 0 and f(x) = 4

∴ $4=a(b)^{0}$

- Remember that any number to the power of zero equal 1

except the zero

∵ $b^{0}=1$

∴ 4 = a(1)

∴ a = 4

Substitute the value of a in the equation

∴ $f(x)=4(b)^{x}$

- Chose any other point fro the table to find b, lets take (1 , 2)

∵ x = 1 and f(x) = 2

∴ $2=4(b)^{1}$

∴ 2 = 4 b

- Divide both sides by 4

∴ $b=\frac{2}{4}=\frac{1}{2}$

- Substitute the value of b in the equation

∴ $f(x)=4(\frac{1}{2})^{x}$

The exponential function which represented by the values in the table is $f(x)=4(\frac{1}{2})^{x}$

Learn more:

You can learn more about the logarithmic functions in brainly.com/question/11921476

#LearnwithBrainly

8 0

2 years ago

Read 2 more answers

The heights of women aged 20 to 29 are approximately normal with mean 64 inches and standard deviation 2.7 inches. Men the same

san4es73 [151]

Answer:

Step-by-step explanation:

$Z=\frac{x-mu}{\sigma }$

X - Heights of women aged 20 to 29: X is N(64, 2.7)

Y - Heights of men aged 20 to 29: X is N(69.3, 2.8)

a) X=6'=72"

Z= $\frac{72-64}{2.7} =2.963$

b) Y = 72"

z= $\frac{72-69.3}{2.8} =0.965$

c) 72' women can be taken as very tall but men moderately taller than average

d) Y<5'5" =65"

Z< $\frac{65-69.3}{2.8} =-1.536$

e) X>73"

Z> $\frac{73-64}{2.7} =3.33$

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5 0

3 years ago

Plz help pretty easy

cricket20 [7]

a and d b and c that's the answer

4 0

3 years ago

Read 2 more answers

Plz help me!!!!!!!!!

Over [174]

Answer: $\bold{\dfrac{4\pm \sqrt{6}}{2}}$

Step-by-step explanation:

$\dfrac{3}{y-2}-2=\dfrac{1}{y-1}\\\\\\\text{Multiply by the LCD (y-2)(y-1) to clear the denominator:}\\\\\dfrac{3}{y-2}(y-2)(y-1)-2(y-2)(y-1)=\dfrac{1}{y-1}(y-2)(y-1)\\\\\\3(y-1)-2(y-2)(y-1)=1(y-2)\\\\3y-3-2(y^2-3y+2)=y-2\\\\3y-3-2y^2+6y-4=y-2\\\\-2y^2+9y-7=y-2\\\\0=2y^2-8y+5\quad \rightarrow \quad a=2,\ b=-8,\ c=5\\\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-8)\pm \sqrt{(-8)^2-4(2)(5)}}{2(2)}\\\\\\.\ =\dfrac{8\pm \sqrt{64-40}}{2(2)}$

$.\ =\dfrac{8\pm \sqrt{24}}{2(2)}\\\\\\.\ =\dfrac{8\pm 2\sqrt{6}}{2(2)}\\\\\\.\ =\dfrac{4\pm \sqrt{6}}{2}$

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2 years ago

What’s the inverse of 4x + 12

stiks02 [169]

Answer:

1/4x -3

Step-by-step explanation:

To find the inverse of a function, exchange x and y and then solve for y

y =4x+12

Exchange x and y

x = 4y+12

Solve for y

Subtract 12 from each side

x-12 = 4y+12-12

x-12 = 4y

Divide by 4

(x-12)/4 = 4y/4

The inverse is

1/4x -3

8 0

2 years ago