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
for any choice of 
. 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
The Order of magnitude for the population of the world is not five
Answer:Justin plans to spend $20 on sports cards. Regular cards cost $3.50 per pack and foil cards cost $4.50 per pack
number of packs of regular cards =r and the number of packs of foll cards = f
Cost of Regular card = 3.50
Cost of 'r' packs of regular card = 3.50r
Cost of Foil card = 4.50
Cost of 'f' packs of Foil card = 4.50f
Justin plans to spend $20 on sports cards so the sum of cost of regular and Foil cards should be less than or equal to 20
The inequality becomes
3.50r + 4.50f <= 20
Answer:
99 Sorry if im wrong
Step-by-step explanation:
The number of bars which can be cut for the 1" X 1" and 2" X 2" square bars are; 117 and 29 units respectively.
<h3>How many bars can be cut from the pan in each case?</h3>
The total area of the given pan can be evaluated as follows;
Area = length × width
= 9 × 13
= 117 square units.
Hence, the number of 1" X 1" bars can be cut which can be cut from the pan;
= 117/(1×1)
= 117 1" X 1" bars.
For the 2" X 2" square bars, we have;
= 117/(2×2);
29 remainder 1 square unit.
Ultimately, one square unit of the pan is wasted for the 2" X 2" square bars.
Read more on area;
brainly.com/question/8294080
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