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## Monday, April 30, 2012

## Tuesday, April 24, 2012

3^(2x + 1) = 27^(3x)

We can solve this by getting a common base and setting the exponents equal to each other. We know that 3^3 = 27, therefore..

3^(2x + 1) = 3^(9x)

Now that the bases are the same (3), we set the exponents equal to each other and solve for x.

2x + 1 = 9x

1 = 7x

1/7 = x

We can also solve this problem by taking the log of both sides and using rules for logarithms.

log(3^(2x + 1)) = log27^3x

(2x + 1)log3 = (3x)log27

(2x + 1)/3x = log27/log3

(2x + 1)/3x = 3

9x = 2x + 1

1 = 7x

1/7 = x

In this problem is was simpler to get a common base. Sometimes it's quite difficult to get a common base. In those cases it's easier to take the log of both sides first.

## Thursday, April 19, 2012

## Monday, April 16, 2012

No matter how large a circle is, the circumference divided by the diameter is equal to Pi.

## Sunday, April 15, 2012

## Thursday, April 12, 2012

## Tuesday, April 10, 2012

If we solve using logarithms, take the log of both sides to get

log (3^(2x+1)) = log(9^(3x + 2))

(2x + 1)log3 = (3x + 2)log9

(2x + 1)/(3x + 2) = log9/log3

(2x + 1)/(3x + 2) = 2

(2x + 1) = 2(3x + 2)

2x + 1 = 6x + 4

-4x = 3

x = -3/4

## Saturday, April 7, 2012

52!/(5! 47!) can be simplified to (52 * 51 * 50 * 49 * 48)/(5 * 4 * 3 * 2) = 2,598,960. That's how many possible 5 card hands can be dealt.

Then we just figure out the number of ways the certain hand you are looking for can be dealt and divide that by 2,598,960 to obtain the probability of obtaining such a hand.

## Thursday, April 5, 2012

4
∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 = 4

^{10}= 1,048,576 ways to answer the 10 multiple choice questions.
If each question has only 1 correct answer and you guess on every one, you have a 1 in 1,048,576 chance of getting a perfect score..

Better start studying!!

## Monday, April 2, 2012

If the problem is 2/sqrt(3), multiply the numerator and denominator by sqrt(3)/sqrt(3) to get

2sqrt(3)/3.

If the problem involves a cube root, multiply the numerator and denominator by whatever will give you a perfect cube in the denominator.

For example, if the denominator is cube root(3), multiply numerator and denominator by cube root(9). This will make the denominator cube root(27), which equals 3.

Same idea for 4th root, 5th root and so on.

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