Write log3 6 as a logarithm of base 2.1) (log2)3/(log2)6
2) (log2)6/(log2)3
3) (log3)2/(log6)2
4) (log6)2/ (log3)2 ...?

Answers

Answer 1

Answer: The answer is 2) (log2)6/(log2)3.

Use the change-of-base formula: $log_a(x)= (log_b(x))/(log_b(a))$

So, if we want to write log3(6) as a logarithm of base 2, in these example a = 3, x = 6, b = 2:
$log_3(6)= (log_2(6))/(log_2(3))$

Answer 2

Answer:

The correct expression for log3 6 as a logarithm of base 2 is option 1) (log₂ 3) / (log₂ 6).

To express log₃ 6 as a logarithm of base 2, we can use the change of base formula. The change of base formula states that logb x = (logc x) / (logc b), where c is any positive value other than 1.

Applying the change of base formula to log3 6:

log₃ 6 = (log₂ 6) / (log₂ 3)

Therefore, the correct expression for log3 6 as a logarithm of base 2 is option 1) (log₂ 3) / (log₂ 6).

To calculate it properly, we need to find the decimal approximation of this expression:

Using the appropriate logarithmic functions, we have:

(log₂ 3) / (log₂ 6) ≈ 1.58496 / 2.58496 ≈ 0.6124

Thus, log₃ 6 as a logarithm of base 2 is approximately 0.6124.

To know more about logarithm:

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Greenland, the largest island in the world, is 21 times larger than Iceland. The combined area of Greenland and Iceland is 880,000 mi2. Write an equation to find the area of Greenland. (Use g to represent the area of Iceland.)

Answers

Greenland is x
Iceland is g

g + x = 880,000
x = 21g

Solve both equations for x (Greenland)
x = 880,000 - g
x = 21g

Because of the transitive property, which states that for any real numbers a, b, and c: If a = b and b = c, then a = c, you can set the two things that equal x equal to each other.
21g = 880,000 - g

Then you simplify.
21g = 880,000 - g
21g + g = 880,000 -g +g
22g = 880,000

Estimate 5,738,055×32

Answers

5738055(32)= 183,617,760
When it said to estimate it basically means to solve.

How the expressions 27 and 2.7 alike

Answers

27 is 2.7 times 10 and 2.7 is 27 ÷ 10

You originally draw a design for an art contest on a 2 in. x 5 in. card. The second phase of the contest requires the drawing to be transferred to an 8.5 in x 11 in. standard sheet of paper and utilize as much of the space on the paper as possible. You determine that the largest size one of the dimensions of your drawing can be is 10.5 in. What is the length of the other dimension if the two drawings are similar? Type your exact answer in the blank without the units, and round to the nearest tenths.

Answers

The correct answer is:
4.2 inches.

Explanation:
We use the size of the largest dimension of the reproduction to find the scale factor. The largest dimension of the original drawing was 5 inches.
The largest dimension of the reproduction is 11 inches.

To find the scale factor, divide:
$(11)/(5)$ =2.1.

Since the scale factor is 2.1, to find the smallest dimension of the reproduction we multiply the original by 2.1:
2*2.1=4.2 inches.

Answer:

Answer is 4.2 - I just took the quiz

Step-by-step explanation:

Each month mrs. li pays her phone company $28 for phone service and$0.07 per minute for long-distance calls. use the expression 28 0.07 m to find the amount she was billed if her long-distance calls totaled 223 minutes.

Answers

To find the amount Mrs. Li was billed for her long-distance calls totaling 223 minutes, you can use the expression:

28 + 0.07 * 223

First, calculate the cost of the long-distance calls:

0.07 * 223 = 15.61

Now, add this cost to the fixed monthly charge:

28 + 15.61 = 43.61

So, Mrs. Li was billed $43.61 for her phone service with 223 minutes of long-distance calls.

A pet survey found that the ratio of dogs a cats is 2/5. Which proportion shows the number of dogs if the number of cats is 140?