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Genrish500 [490]
3 years ago
5

3

Mathematics
1 answer:
Marianna [84]3 years ago
6 0

The expression into a single logarithm is log[(x)^{10}][(2)^{30}]

Step-by-step explanation:

Let us revise some logarithmic rules

  • log(a)^{n}=nlog(a)
  • log(ab)=log(a)+log(b)
  • nlog(a)+mlog(b)=log[(a)^{n}][(b)^{m}]

∵ 10 log(x) + 5 log(64)

- At first re-write 10 log(x)

∴  10 log(x) = log(x)^{10}

- Then re-write 5 log(64)

∴  5 log(64) = log(64)^{5}

∴ 10 log(x) + 5 log(64) = log(x)^{10} + log(64)^{5}

- Use the 3rd rule above to make it single logarithm

∵ log(x)^{10} + log(64)^{5} = log[(x)^{10}][(64)^{5}]

∴ 10 log(x) + 5 log(64) = log[(x)^{10}][(64)^{5}]

∵ 64 = 2 × 2 × 2 × 2 × 2 × 2

∴ We can write 64 as 2^{6}

∴ (64)^{5}=(2^{6})^{5}

- Multiply the two powers of 2

∴ (64)^{5}=(2)^{30}

∴ 10 log(x) + 5 log(64) = log[(x)^{10}][(2)^{30}]

The expression into a single logarithm is log[(x)^{10}][(2)^{30}]

Learn more:

You can learn more about the logarithmic functions in brainly.com/question/11921476

#LearnwithBrainly

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NISA [10]

6x/6=x>/= (=) 11/6

x=11/6 or about 1.8

the first important notation to remember when graphing inequalities is that the graph is going to face the way the inequality sign is pointing.

in this case, the sign is pointing right. now the second thing to remember is that an inequality sign with a line underneath it means that it is greater/equal to so the graph in which we fill will have be a closed circle

1) start the ray at ~1.8 and fill in the circle at the end of the ray then extend to its endpoint

that's all. you're graph now reads  x is greater or equal to 11/6

3 0
3 years ago
Write the equation of the line parallel to 2x - 6y = 12 that passes through the point ( -1, 4).​
vlada-n [284]

Answer:

y = 1/3x + 4 1/3

Step-by-step explanation:

2x - 6y = 12

First find the slope

Solve for y

Subtract 2x

2x - 6y -2x= 12-2x

-6y = -2x+12

Divide by -6

-6y/-6 =-2x/-6 +12/-6

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The slope is 1/3

Parallel lines have the same slope

Using the slope intercept form y = mx+b where m is the slope and b is the y intercept

y = 1/3x +b

And substituting in the point

4 = 1/3 (-1) +b

4 = -1/3 +b

Add 1/3 to each side

4 + 1/3 = b

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3 years ago
5b-2=13 what does b equal
Alex777 [14]
5b-2=13  add 2 to both sides

5b=15  divide both sides by 5

b=3
6 0
3 years ago
Read 2 more answers
. (1 pt) A store sold 330 yards of fabric. It charged $11 a yard. What is the total cost of the fabric?
stellarik [79]
Hey there

So 330/11=30
<span>so the total cost is 30 $</span>
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Step-by-step explanation:

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