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prisoha [69]
2 years ago
11

Write the equation 6561 1/4= 9 in logarithmic form.

Mathematics
1 answer:
Vlad1618 [11]2 years ago
8 0

Answer:

  b. log6561(9) = 1/4

Step-by-step explanation:

The relationship between the exponential form and the log form is ...

  b^n=x\\\log_b{(x)}=n

The exponent is the logarithm. The base is the value the exponent is being applied to.

Here, you have ...

  6561^{\frac{1}{4}}=9

Comparing this to the form above, we see ...

  b = 6561, n = 1/4, x = 9

so the log form of the equation is ...

  \boxed{\log_{6561}{(9)}=\frac{1}{4}}

This matches choice B.

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Step 1

Find the perimeter of rectangle ABDE

we know that

the perimeter of rectangle is equal to

P=2b+2h

In this problem

b=ED=2\ units

h=AE=6\ units

substitute

P=2*2+2*6=16\ units  

Step 2

Find the perimeter of triangle BCD

we know that

the perimeter of triangle is equal to

P=BD+DC+BC

In this problem we have

BD=AE=6\ units

DC=BC

Applying the Pythagoras theorem

DC^{2}=4^{2}+3^{2}

DC^{2}=25

DC=5\ units

substitute

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Find the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD

we have

the perimeter of rectangle is equal to

P=16\ units  

the perimeter of the triangle is

P=16\ units  

so

the ratio is equal to

\frac{16}{16} =1

therefore

<u>the answer Part 1) is the option B</u>

1

Step 3

Find the area of polygon ABCDE

we know that

The area of polygon is equal to the sum of the area of rectangle plus the area of triangle

Area of rectangle is equal to

A=AE*BD=6*2=12\ units^{2}

Area of the triangle is equal to

A=\frac{1}{2}AEh

the height h of the triangle is equal to 4\ units

substitute

A=\frac{1}{2}(6)(4)=12\ units^{2}

The area of polygon is

12\ units^{2}+12\ units^{2}=24\ units^{2}

therefore

<u>the answer part 2) is the option C</u>

24\ units^{2}


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