Please answer, I would be happy :)

UNO [17]

What is log675 with base 5 × log 3 with base 3?
We have to calculate (log 675 to the base 5) × (log 3 to the base 3)

Note the following important points :

(1.) log 675 to the base 5

=> log 675 to the base ‘e’ / log 5 to the base ‘e’

=> ln 675 / ln 5

Since 675 = 5^2 × 3^3

=> ln 675 = ln [5^2 × 3^3]

=> ln (5^2) + ln (3^3)

=> 2 ln 5 + 3 ln 3

Hence, log 675 to the base 5

= ln 675 / ln 5

= [2ln 5 + 3ln 3] / ln 5

(2.) Similarly, log 3 to the base 3

=> Since the logarithm of any natural number 'x' to the base of same number 'x' is always 1 (since any natural number raised to the power '1′ is equal to the same number) ,

Thus, (log 3 to the base 3) = 1

Hence, our problem reduces to:

(log 675 to the base 5) × (log 3 to the base 3)

=> [(2ln 5 + 3ln 3) / ln 5] × (1)

=> (2ln 5 + 3ln 3) / ln 5

=> So we only require the values of natural logarithm of 3 and 5 :)

We should remember these values, or we can always use log table.

Since ln 3 = 1.098

and ln 5 = 1.609

=> 2ln 5 = 2(1.609) = 3.218

=> 3ln 3 = 3(1.098) = 3.294

Hence,

solution : (3.218 + 3.294) / 1.609

=> 6.512 / 1.609

=> 4.047

GLAD TO HELP YOU ;))

8 0

3 years ago

Cameron is a member of a national gardening club. she asked 200 of her fellow members whether they use compost to fertilize thei

krok68 [10]

Using the z-distribution, it is found that the 90% confidence interval for the true proportion of club members who use compost is (0.392, 0.508).

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

In this problem, we have a 90% confidence level, hence $\alpha = 0.9$ , z is the value of Z that has a p-value of $\frac{1+0.9}{2} = 0.95$ , so the critical value is z = 1.645.

The estimate and the sample size are given by:

$\pi = 0.45, n = 200$

Hence, the bounds of the interval are:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 - 1.645\sqrt{\frac{0.45(0.55)}{200}} = 0.392$

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 + 1.645\sqrt{\frac{0.45(0.55)}{200}} = 0.508$

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ4

4 0

2 years ago

Read 2 more answers

How do you work out 49.2 x 10.3

kirza4 [7]

You line 49.2
×10.3
---------
506.76

7 0

4 years ago

Two workers can make two chairs in two days. How many chairs can 8 workers working at the same rate make in 20 days?

Vlad [161]

So we know that 2 workers can make 2 chairs in 2 days. Therefore if we use that same proportion, we will find that 8 workers can make 8 chairs in 2 days.

But the question is asking for 20 days, so we must multiply this by 10.

So, when we multiply 8 by 10, we find that in 20 days, 8 workers can make 80 chairs.

7 0

3 years ago

Leon measured the distance each of his four toy cars rolled across the floor. Which car measurement that has a 4 in the thousand

Kobotan [32]

0.714 and so does 0.224 has 4 in the thousandths place, but in shortest distance I believe it is 0.714

8 0

3 years ago