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irga5000 [103]
2 years ago
5

Rewrite the following expression using the properties of loy

Mathematics
2 answers:
andrew-mc [135]2 years ago
7 0

Answer:

\log_2\dfrac{x^2z}{y^2}+\log_9x^{12}y^4

Step-by-step explanation:

<u>Log laws</u>

\textsf{Product law}: \quad \log_axy=\log_ax + \log_ay

\textsf{Quotient law}: \quad \log_a\frac{x}{y}=\log_ax - \log_ay

\textsf{Power law}: \quad \log_ax^n=n\log_ax

Given expression:

\log_2z+2\log_2x+4\log_9y+12\log_9x-2\log_2y

Group terms with same log base:

\implies \log_2z+2\log_2x-2\log_2y+4\log_9y+12\log_9x

Apply the power law:

\implies \log_2z+\log_2x^2-\log_2y^2+\log_9y^4+\log_9x^{12}

Apply the product law:

\implies \log_2x^2z-\log_2y^2+\log_9x^{12}y^4

Apply the quotient law:

\implies \log_2\dfrac{x^2z}{y^2}+\log_9x^{12}y^4

Dimas [21]2 years ago
6 0

\\ \rm\Rrightarrow log_2z+2log_2x+4log_9y+12log_9x-2log_2y

  • log_a^b=bloga
  • log_a(bc)=log_a b+log_a c

So

\\ \rm\Rrightarrow log_2z+log_2x^2-log_2y^2+log_9y^4+log_9x^{12}

\\ \rm\Rrightarrow log_2(zx^2)-log_2y^2+log_9(y^4x^{12})

\\ \rm\Rrightarrow log_2\left(\dfrac{zx^2}{y^2}\right)+log_9(y^4x^{12})

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D. 62 square feet

Step-by-step explanation:

uz + wx + (v+z)(y-u-w)

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18 + 24 + 20 = 62

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5×(4+3)=5×4+5×3 which number of property is shown above? A.associative property B.communative property C.distributive property D
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What is the area of the triangle?<br> 12<br> 8
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Step-by-step explanation:

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3 years ago
Read 2 more answers
Plz answer this correctly.....plzzzzz quickly......:)<br>&lt;3.....​
kramer

Answer:

31.01, 180.8, 0.2, 15501

Step-by-step explanation:

Puzzle 1:

The first rule takes out 301

The second rule has to have a 1 in the units place so that takes out 3.1, 3.101, and 30.1

The 3rd rule takes out 1.01, and 1.03

Rule 4, is self explanatory, so it takes out 31.3

and the last rule takes out 31.1 bc there is no hundredths column

That leaves you with 31.01

Puzzle 2:

Rule 1 takes out 18180

Rule 2, self explanatory, takes out 180

Rule 3 takes out numbers less than 18 so 1.81 and 0.18

Rule 4 takes out  18.01, 1800, 188, and 18.8

That leaves you with 180.8

Puzzle 3:

Rule 1 takes out 0.24, 0.5, and 2.02

Rule 2 takes out 0.15

Rule 3 takes out 0.02, 0.01 and 0.1 (bc it just says greater than and not equal to so it takes this one out)

Rule 4 takes out 0.12

That leaves you with 0.2

Puzzle 4:

Rule 1 takes out 45000

Rule 2 takes out 5401, 5444, and 4544

Rule 3 takes out 5454

Rule 4 does not take out any because all the remaining numbers ( 14500, 15501, 14534, and 10500) have 5 hundreds

Rule 5 takes out 14500, 14534, and 10500

That leaves you with 15501

Hope this helped :)

5 0
2 years ago
The radius of a circle is 6 miles. What is the circle's area?<br> Use 3,14 for pi
ICE Princess25 [194]

Answer: 28.6 miles

Step-by-step explanation:

A = pi r^2

A = 3.14 (3)^2

Now multiply 3.14(3)^3

Your answer is 28.26

* Radius is 1/2 of the diameter.

I believe this is right, but im not sure.

Hope it helps :)

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3 years ago
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