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Margarita [4]
2 years ago
7

3√7 please help I dont understand

Mathematics
1 answer:
UNO [17]2 years ago
8 0
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 ;))
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-8x-27=-7\left(1+2x\right)+2x

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2 years ago
In ΔMNO, m∠M = 57° and m∠N = 75°. Which list has the sides of ΔMNO in order from shortest to longest?
gulaghasi [49]

Answer:

B. MN, NO, OM

Step-by-step explanation:

Recall: In any triangle, the sides and the angles are related in the following way:

*The largest angle and the longest side are opposite each other

*The medium angle and the mid-sized side are opposite each other

*The smallest angle and the shortest side are opposite each other

In ∆MNO, we are given that

m<M = 57° which is opposite to side NO

m<N = 75° which is opposite to side OM

m<O = 180° - (75° + 57°) (sum of triangle)

m<O = 48° which is opposite to side MN

Therefore, we can write the order of shortest to longest side in relation to their opposite angles as follows:

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The price after the discount is $3.706

<h3>Discount price</h3>

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Price after the discount = $4.36 - 0.654

Price after the discount = $3.706

Hence the price after the discount is $3.706

Learn more on discount here: brainly.com/question/24304697

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