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2^(3x-5)=1/2^(2x-10) Find x.

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afrokaa | Student, College Freshman | (Level 2) Honors

Posted December 4, 2010 at 2:09 AM via web

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2^(3x-5)=1/2^(2x-10) Find x.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted December 4, 2010 at 2:10 AM (Answer #1)

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We have to find x, given that  2^(3x-5) = 1/2^(2x-10).

Now 2^(3x-5) = 1/2^(2x-10)

=> 2^(3x - 5) = 2^ -(2x - 10)

Now as the base is the same , we can equate the exponent terms.

=> (3x - 5) = -(2x - 10)

=> 3x - 5 = -2x + 10

=> 3x + 2x = 10 + 5

=> 5x = 15

=> x = 15/5

=> x = 3

Therefore x is equal to 3.

To check 2^(3x-5)  = 2^ (9 - 5 ) = 2^4

1/2^(2x-10) = 1/2^(2*3 - 10) = 2^ - 4 = 2^4

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neela | High School Teacher | (Level 3) Valedictorian

Posted December 4, 2010 at 2:14 AM (Answer #2)

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2^(3x-5) = 1/2^(2x-10).

To find x:

We rewite the right side as 2^-(2x-10) = 2^(10-2x), as 1/a^m = a^(-m) by the law of exponents.

Therefore ,

2^(3x-5) = 2^(10-2x). Both sides are the eexponents of the same base. Therefore exponents are equal.

3x-5 = 10-2x.

3x+2x = 10+5

5x= 15.

x = 15/5 = 3.

x= 3.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted December 4, 2010 at 2:09 AM (Answer #3)

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Given that: 2^(3x-5) = 1/2^(2x-10)

We will re-wrtie.

We know from exponent properties that 1/x^a = x^-a.

==> 1/2^(2x-10) = 2^-(2x-10).

Then, we will substitute.

==> 2^(3x-5) = 2^-(2x-10)

Now that we have the bases are equal, then the powers must be equal too.

Then, we conclude that 3x-5 = -(2x-10)

Let us solve the equality.

==> 3x - 5 = -2x + 10

We will add 2x to both sides.

==> 2x+3x - 5 = 2x-2x + 10

==> 5x - 5 = 10

Now we will add 5 to both sides.

==> 5x - 5 +5 = 10 + 5

==> 5x = 15.

Now we will divide by 5.

=> x = 15/5 = 3

Then the answer is x = 3

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted December 4, 2010 at 2:09 AM (Answer #4)

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First, we'll use the negative power property of exponentials:

1/2^(2x - 10) = 2^-(2x-10)

Now, we'll re-write the equation:

2^(3x-5) = 2^-(2x-10)

Since the bases are matching, we'll use one to one property:

3x-5 = -2x+10

We'll isolate x to the left side. For this reason, we'll add 2x both sides:

3x + 2x - 5 = 10

We'll combine like terms and we'll add 5 both sides:

5x = 10 + 5

5x = 15

We'll divide by 5:

x = 3

The solution of the equation is x = 3.

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