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stiv31 [10]
2 years ago
9

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

Mathematics
1 answer:
Andrei [34K]2 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>

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Given the data set (200, 150, 325, 350, 100, 75), Find the range of the data set
andriy [413]
The range is just the distance between the biggest number
and the smallest one.

The biggest number on that list is  350 .
The smallest number on that list is  75 .

The range is from  75 to 350, or a distance of  275 .
4 0
2 years ago
Kaylib’s eye-level height is 48 ft above sea level, and addison’s eye-level height is 85 and one-third ft above sea level. how m
GalinKa [24]

The addison see to the horizon at 2 root 2mi.

We have given that,Kaylib’s eye-level height is 48 ft above sea level, and addison’s eye-level height is 85 and one-third ft above sea level.

We have to find the how much farther can addison see to the horizon

<h3>Which equation we get from the given condition?</h3>

d=\sqrt{\frac{3h}{2} }

Where, we have

d- the distance they can see in thousands

h- their eye-level height in feet

For Kaylib

d=\sqrt{\frac{3\times 48}{2} }\\\\d=\sqrt{{3(24)} }\\\\\\d=\sqrt{72}\\\\d=\sqrt{36\times 2}\\\\\\d=6\sqrt{2}....(1)

For Addison h=85(1/3)

d=\sqrt{\frac{3\times 85\frac{1}{3} }{2} }\\d\sqrt{\frac{256}{2} } \\d=\sqrt{128} \\d=8\sqrt{2} .....(2)

Subtracting both distances we get

8\sqrt{2}-6\sqrt{2}  =2\sqrt{2}

Therefore, the addison see to the horizon at 2 root 2mi.

To learn more about the eye level visit:

brainly.com/question/1392973

5 0
2 years ago
Kalani bought 2.5 pounds oranges for $1.58 per pound.how much did kalani spend on oranges ?
Tcecarenko [31]

To find the answer for this simply multiply 2.5 by 1.58

2.5 x 1.58= 3.95

So Kalani spent a total of $3.95 on oranges!

6 0
3 years ago
Read 2 more answers
I dont know this i dont understand can someone help me? please thank you​
emmasim [6.3K]

Answer:

hope that will help you

7 0
3 years ago
HURRY! please help i’ll give brainliest
Darya [45]

Answer:

The first and third options.

Explanation:

Look at each column and add the number of families.

6 0
3 years ago
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