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What is the value of x which satisfies...

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parama9000 | Student, Grade 11 | Valedictorian

Posted May 24, 2013 at 3:34 AM via web

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What is the value of x which satisfies

2^1995+2^1995+2^1995+2^1995+2^1995+2^1995+
+2^1995+2^1995=2^x

a.1996 b.1997 c.1998 d.1999 e.2000

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crmhaske | College Teacher | (Level 3) Associate Educator

Posted May 24, 2013 at 3:44 AM (Answer #1)

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`2^1995+2^1995+2^1995+2^1995+2^1995+2^1995+2^1995+2^1995=2^x`

We can simplify this problem as:

`8(2^1995)=2^x`

We know that 8=2^3 theregore:

`(2^3)(2^1995)=2^x`

Following the rule of exponenets that state the following:

`x^mx^n=x^(m+n)`

Therefore:

`(2^3)(2^1995)=2^(3+1995)=2^1998=2^x`

Therefore, x=1998, so the answer is c.

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crmhaske | College Teacher | (Level 3) Associate Educator

Posted May 24, 2013 at 3:45 AM (Reply #1)

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*therefore

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