Ask question

Ask question

All categories

2 years ago

11

Solve for X.

"TexFormula1" title="log_{8} x-log_{8} (-2x+4) = log_{8} 3" alt="log_{8} x-log_{8} (-2x+4) = log_{8} 3" align="absmiddle" class="latex-formula">

2 answers:

taurus [48]2 years ago

4 0

Answer: $x=\frac{12}{7}$

Step-by-step explanation:

Remember the logarithms properties:

$log(m)-log(n)=log(\frac{m}{n})\\\\b^{log_b(a)}=a$

Then,simplifying:

$log_{8}(\frac{x}{-2x+4}) = log_{8}(3)$

Apply base 8 to boths sides and then solve for "x":

$8^{log_{8}(\frac{x}{-2x+4})}=8^{log_{8}(3)}\\\\\frac{x}{-2x+4}=3\\\\x=3(-2x+4)\\\\x=-6x+12\\x+6x=12\\7x=12\\\\x=\frac{12}{7}$

ankoles [38]2 years ago

3 0

Answer:

x = 12/7.

Step-by-step explanation:

log8 x - log8 (-2x + 4) = log8 3

Using the law of logs, log a - log b = log (a/b):-

log8 [x / (-2x + 4)] = log8 3

Taking antilogs of both sides:

x / (-2x + 4) = 3

x = -6x + 12

7x = 12

x = 12/7

(answer).

You might be interested in

(143(5) + 67)5 ___________ 2 <br> A. 1950 <br> B. 1955 <br> C. 1956 <br> D. 1953

Charra [1.4K]

The Correct Answer Is B 1955

4 0

2 years ago

Can you ask 5 people to name as much states in 60 seconds please?

Lyrx [107]

Answer:

Alabama, Alaska, American Samoa, Arizona, Arkansas.

California, Colorado, Connecticut.

Delaware, District of Columbia.

Florida.

Georgia, Guam.

Hawaii.

Idaho, Illinois, Indiana, Iowa.

Kansas, Kentucky.

4 0

2 years ago

I need help please :(

zloy xaker [14]

Answer:

-(1/3 · 1/3 · 1/3 · 1/3 )

Step-by-step explanation:

-(3)^-4= -1/3 ^4 = -1/81

-(1/3 · 1/3 · 1/3 · 1/3 )= -1/81

7 0

3 years ago

Read 2 more answers

While training for a marathon, Jeff wants to increase the number of miles he runs each day. On the first day of training, Jeff r

user100 [1]

Answer:

The series is 5 , 6 , 7 , 8 , 9 , 10 , 11

Step-by-step explanation:

* Lets revise the arithmetic series

- In the arithmetic series there is a constant difference between

each two consecutive numbers

- Ex:

# 2 , 5 , 8 , 11 , ………………………. (constant difference is 3)

# 5 , 10 , 15 , 20 , ………………………… (constant difference is 5)

# 12 , 10 , 8 , 6 , …………………………… (constant difference is -2)

* General term (nth term) of an Arithmetic series:

- If the first term is a and the common diffidence is d, then

U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d

- So the nth term is Un = a + (n – 1)d, where n is the position of the

number in the series

* Lets solve the problem

- Jeff wants to increase the number of miles he runs each day

∴ He will add the initial value by constant number each day

- He plans on increasing the number of miles he runs a day by 1

∴ The constant value is 1 mile

- On the first day of training, Jeff runs 5 miles

∴ The first value is 5 miles

∴ The series is arithmetic

∵ a = 5 , d = 1

- He do that for the remainder of the week

∵ The week has 7 days

∴ The series has 7 terms

∵ The rule of the series is Un = a + (n - 1)d

∵ a = 5 and d = 1

∴ Un = 5 + (n - 1)(1)

∴ Un = 5 + n - 1

∴ Un = 4 + n ⇒ n is the position of the number

- Substitute n from 1 to 7 to find the series

∴ The series is 5 , 6 , 7 , 8 , 9 , 10 , 11

6 0

3 years ago

Here are the vertices of rectangle FROG: (-2,5),(-2,1),(6,5),(6,1). Find the perimeter of this rectangle. If you get stuck, try

ryzh [129]

Answer:

Part 1) The perimeter of rectangle is equal to 24 units

Part 2) The area of rectangle is equal to 32 square units

Step-by-step explanation:

Part 1) Find the perimeter of rectangle

we know that

The perimeter of rectangle is equal to

$P=2(L+W)$

where

L is the length of rectangle

W is the width of rectangle

we have

$F(-2,5),R(-2,1),O(6,1),G(6,5)$

Plot the figure to better understand the problem

using a graphing tool

see the attached figure

Remember that in a rectangle opposite sides are congruent and the measure of each interior angle is equal to 90 degrees

so

$FG=RO=L\\RF=OG=W$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the distance FG

$F(-2,5),G(6,5)$

substitute the values

$d=\sqrt{(5-5)^{2}+(6+2)^{2}}$

$d=\sqrt{(0)^{2}+(8)^{2}}$

$FG=8\ units$

step 2

Find the distance RF

$R(-2,1),F(-2,5)$

substitute the values

$d=\sqrt{(5-1)^{2}+(-2+2)^{2}}$

$d=\sqrt{(4)^{2}+(0)^{2}}$

$RF=4\ units$

step 3

Find the perimeter

$P=2(L+W)$

we have

$FG=RO=L=8\ units\\RF=OG=W=4\ units$

substitute

$P=2(8+4)=24\ units$

Part 2) Find the area of rectangle FROG

we know that

The area of rectangle is equal to

$A=LW$

we have

$FG=RO=L=8\ units\\RF=OG=W=4\ units$

substitute

$A=(8)(4)=32\ units^2$

8 0

2 years ago