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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>

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Answer: 4.21596 x 10⁴⁷

<u>Step-by-step explanation:</u>

  (3.346 x 10²⁶) (1.26 x 10²¹)

= (3.346 x 1.26) x 10²⁶⁺²¹

= 4.21596 x 10⁴⁷

8 0
3 years ago
The radius of a cylindrical water tank is 6.5 ft, and its height is 19 ft. What is the volume of the tank?
creativ13 [48]

Answer:

The volume of the cylinder is 2520.64ft³

Step-by-step explanation:

To calculate the volume of a cylinder we have to use the following formula:

v = volume

h = height = 19ft

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r = radius = 6.5ft

v = (π * r²) * h

we replace with the known values

v = (3.14 * (6.5ft )²) * 19ft

v = (3.14 * 42.25ft²) * 19ft

v = 132.665ft² * 19ft

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4 0
3 years ago
Can i get its answer?​
Komok [63]

Yo sup??

perimeter=2(l+b)

100=2(35+b)

b=15 cm

area=b*h

=35*15

=525 cm²

Hope this helps

4 0
3 years ago
Read 2 more answers
The graph of the equation y=x^2-7 is symmetric with respect to which of the following?a.the line y=-x+7b.the y-axis c.the x axis
lys-0071 [83]

Answer:

b

Step-by-step explanation:

since coefficient of x = 0

5 0
3 years ago
11.(02.03)
Marianna [84]

Answer:

step number 1 is incorrect.

Step-by-step explanation:

Here is the solution of this equation [2x-31-1=2].

2x-31-1=2

or 2x-31=2+1

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or 2x= 34

or x=34/2

or x= 17

the answer of this equation is X=17.

8 0
2 years ago
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