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3 years ago

Write the expression as a sum and/or a difference of logarithms, with all variables to the first degree.

Mathematics

1 answer:

andreyandreev [35.5K]3 years ago

7 0

Answer:

ln 2 + 2 ln x + 8 ln y

Step-by-step explanation:

Use of properties

log ab = log a + log b
log a^b = b log a

Given expression

In 2x^2y^8

Simplifying

In 2x^2y^8 =
ln 2 + ln x^2 + ln y^8 =
ln 2 + 2 ln x + 8 ln y

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Show work and explain with formulas:

Marina86 [1]

17 Answer: 205

Step-by-step explanation:

$\{1\dfrac{2}{3}+1\dfrac{5}{6}+2+...+8\dfrac{1}{3}\}\implies a_1=1\dfrac{2}{3},\ d=\dfrac{1}{6}\\\\\\a_n=a_1+d(n-1)\qquad solve\ for\ n\\\\8\dfrac{1}{3}=1\dfrac{2}{3}+\dfrac{1}{6}(n-1)\\\\\\\dfrac{25}{3}=\dfrac{5}{3}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{50}{6}=\dfrac{10}{6}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{41}{6}=\dfrac{1}{6}n\\\\\\\dfrac{41}{6}\cdot 6=n\\\\41=n$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{41}=\dfrac{1\dfrac{2}{3}+8\dfrac{1}{3}}{2}\cdot 41\\\\\\.\quad =\dfrac{10}{2}\cdot 41\\\\\\.\quad =5\cdot 41\\\\.\quad =\large\boxed{205}$

18 Answer: 1968

Step-by-step explanation:

$a_1=-6,\ d=2,\ n=48, \quad \text{solve for }a_{48}\\\\a_{n}=a_1+d(n-1)\\\\a_{48}=-6+2(48-1)\\\\.\quad =-6+2(47)\\\\.\quad =-6+94\\\\.\quad =88$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{48}=\dfrac{-6+88}{2}\cdot 48\\\\\\.\quad =\dfrac{82}{2}\cdot 48\\\\\\.\quad =41\cdot 48\\\\.\quad =\large\boxed{1968}$

19 Answer: -116

Step-by-step explanation:

$\{3, -2, -7, ...\}\\a_1=3,\ d=-5,\ n=8, \quad \text{solve for }a_{8}\\\\a_{n}=a_1+d(n-1)\\\\a_{8}=3-5(8-1)\\\\.\quad =3-5(7)\\\\.\quad =3-35\\\\.\quad =-32\\\\\text{Now use the sum formula:}\\\\S_8=\dfrac{a_1+a_8}{2}\cdot 8\\\\\\S_{8}=\dfrac{3-32}{2}\cdot 8\\\\\\.\quad =\dfrac{-29}{2}\cdot 8\\\\\\.\quad =-29\cdot 4\\\\.\quad =\large\boxed{-116}$

6 0

3 years ago

Solve for x. x+23=−22 someone help

BaLLatris [955]

Answer:

x = - 45

Step-by-step explanation:

x+23(-23)=−22 (-23)First subtract 23 from both sides

x = - 45

7 0

3 years ago

Answer with figure if needed.random answer will be reported.

max2010maxim [7]

10m/s

32m/s

83m/s

None of these

Answer :

Solution :

At any instant x2+y2=52

Differentiating w.r.t. time 2xxdt+2ydydt=0

Here dxdt=2,dydt=u⇒u=83m/s

8 0

3 years ago

Deepak wrote out the steps to his solution of the equation – 3x – 5 + 4x = –.

MrMuchimi

X=5 if that's what you were asking for

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3 years ago

PLEASE HELPPP :(( lol

Ksivusya [100]

Answer:

the pic is block

Step-by-step explanation:

7 0

3 years ago