1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
stiv31 [10]
3 years ago
9

(1/27)^x-6=27Could I please have a step by step as well? Much appreciated! ​

Mathematics
1 answer:
Andrei [34K]3 years ago
5 0

Answer:

x = 7

Step-by-step explanation:

1) Use Division Distributive Property: (x/y)^a = x^a/y^a.

\frac{1}{ {27}^{x - 8} }  = 27

2) Multiply both sides by 27^x - 8.

1 =  {27} \times 27^{1 + x  - 8}

3) Use the product rule: x^a x^b = x^a+b.

1 =  {27}^{1 + x - 8}

4) Simplify 1 + x - 8 to x - 7.

1  =  {27}^{x - 7}

5) Use Definition of Common Logarithm: b^a = x if and only if log<u>b</u><u> </u>(x) = a.

log_{27}1 = x - 7

6) Use Change of Base Rule.

\frac{ log_1  }{  log{27} }  = x - 7

7) Use rule of 1: log 1 = 0.

\frac{0}{ log_{27}}  = x - 7

8) Simplify 0/log_27 to 0.

0 = x - 7

9) Add 7 to both sides.

7 = x

10) Switch sides.

x = 7

<u>Therefor</u><u>,</u><u> </u><u>the</u><u> </u><u>answer</u><u> </u><u>is</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>7</u><u>.</u>

You might be interested in
The coordinates of point A on a grid are (−1, 6). Point A is reflected across the y-axis to obtain point B. The coordinates of p
-Dominant- [34]

Answer:

(1,6)

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Help me with C number please. Show me how did you do that. It’s due in 30 minutes.
Paha777 [63]
I’m not 100% sure but isn’t it x2 +xy +y2?
6 0
3 years ago
Read 2 more answers
An altitude is drawn from the vertex of an isosceles triangle, forming a right angle
Hatshy [7]

Answer:56.8 inches

Step-by-step explanation:

For perimeter we must find the lengths of the 2 diagonal sides of the triangle which are the same because it is isosceles.

the triangle is cut directly in half so both halves of the base are 17/2

17/2 = 8.5

solve through pythagoren theorum

altitude^2 + (half of base)^2 = (diagonal length)^2

18^2 + (8.5)^2 = (diagonal length)^2

324 + 72.25 = (diagonal length)^2

396.3 = (diagonal length)^2

\sqrt{396.3} = diagonal length

diagonal length = 19.9

diagonal length + diagonal length + base = perimeter

19.9 + 19.9 + 17 = perimeter

56.8 inches = perimeter

6 0
2 years ago
Jernel has to figure out the area of her square garage. she knows that one side of the garage is equal to the length of her rabb
Readme [11.4K]

Answer: 100 square units.

Step-by-step explanation:

Given: Jernel has to figure out the area of her square garage.

She knows that one side of the garage is equal to the length of her rabbit pen.

Now, the length of the rabbit pen = 10 units

Then , the length of the garage will be 10 units

Now, Area of square = \text{(side)}^2=10^2=100\text{units}^2

Hence, the area of the garage = 100 square units.

4 0
3 years ago
Question 2:
Aleonysh [2.5K]
15 minutes each day.
8 0
3 years ago
Read 2 more answers
Other questions:
  • Determine the domain and range for the inverse of f(x)=1/3x - 1
    10·1 answer
  • Miles buys a 10-ounce bag of chips. He weighs it in a scale and makes four measurements. Which measurement is the most accurate
    14·2 answers
  • Silky smooth linens takes out a loan of $2,500, for 314 days. if the amount of interest is $83.29, use the exact interest method
    9·1 answer
  • I don't get what f(-10) means
    11·1 answer
  • $394.63781 Round to the nearest dollar
    13·2 answers
  • A coyote population has decreased by 168 over the past 3 years. The same number of coyotes were lost each year. Which division e
    9·1 answer
  • Draco and his friends bought Bertie Bott's Every Flavor Beans for $3 per packet and chocolate frogs for $1 per packet at Honeydu
    15·1 answer
  • A right triangle has legs that are 10 yards and 12 yards
    12·1 answer
  • Simplify 4 ^ 9 x 4 ^ 3​
    10·1 answer
  • Solve for L:<br> P=2L+2W
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!