We can expand the logarithm of a product as a sum of logarithms:

Then using the change of base formula, we can derive the relationship

This immediately tells us that

Notice that none of  can be equal to 1. This is because
 can be equal to 1. This is because

for any choice of  . This means we can safely do the following without worrying about division by 0.
. This means we can safely do the following without worrying about division by 0.

so that

Similarly,

so that

So we end up with

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Another way to do this:



Then

So we have

 
        
             
        
        
        
Step-by-step explanation:
we know that perimeter of triangle is equals to side + side + side 
but we can see that the particular triangle is having all the sides equal so it is seen to be equal lateral triangle and formula of equilateral triangle is 3 × sides.....
So,We will take sides common.....
 Perimeter of equilateral triangle= 3×Side
 3×4.6 cmsq.
 13.8cmsq. Answer
 
        
             
        
        
        
Answer:
3 square root 2. 
Step-by-step explanation:
I think the answer is b (3 square root 2). the Pythagorean therom states that B^2+ B^2= C^2. we know that c squared is 36. 3 square root 2 is approximately 4.24. ( this squared is 17.98). 17.98 + 17.98 = 35.96.  If i round this up, it is 36. 
 
        
             
        
        
        
<h3>
Answer:   -i</h3>
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Explanation:
i = sqrt(-1)
Lets list out the first few powers of i
- i^0 = 1
- i^1 = i
- i^2 = -1
- i^3 = i*i^2 = i*(-1) = -i
- i^4 = (i^2)^2 = (-1)^2 = 1
By the time we reach the fourth power, we repeat the cycle over again (since i^0 is also equal to 1). The cycle is of length 4, which means we'll divide the exponent over 4 to find the remainder. Ignore the quotient. That remainder will determine if we go for i^0, i^1, i^2 or i^3. 
For example, i^5 = i^1 because 5/4 leads to a remainder 1.
Another example: i^6 = i^2 since 6/4 = 1 remainder 2
Again, we only care about the remainder to find out which bin we land on.
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Turning to the question your teacher gave you, we have,
739/4 = 184 remainder 3
So i^739 = i^3 = -i
<h3>
-i is the final answer</h3>
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Side notes:
- if i^a = i^b, then a-b is a multiple of 4
- Recall that the divisibility by 4 trick involves looking at the last two digits of the number. So i^739 is identical to i^39.