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OG QUESTION # 147

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OG QUESTION # 147

by factor26 » Sat Jul 23, 2011 9:00 am
IF X AND K ARE INTEGERS AND (12^X)(4^2X+1)=(2^K)(3^2), WHAT IS THE VALUE OF K?

(A) 5
(B) 7
(C) 10
(D) 12
(E) 14

OG ANSWER IS E ... CAN SOMEONE PLEASE BREAK DOWN THE CONCEPTS INVOLVED IN SOLVING THIS PROBLEM AND HOW TO SOLVE THIS PROBLEM?

THANKS!!
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by knight247 » Sat Jul 23, 2011 9:24 am
finding it a little difficult to explain all the exponents with the keyboard. Have written down the solution on a piece of paper and have scanned and uploaded it here. Hope it helps.

in step two, I have broken down 12^x as 3^x multiplied by 4^x

in step four, I have multiplied 4^x with 4^2x+1. Remember when two numbers with similar bases are multiplied their similar/dis-similar exponents are only added. Giving us 4^3x+1

in step five, I have expressed 4 as 2^2 inside the bracket. So the exponent outside the bracket is unaffected.

in step six, I have opened up the bracket. Remember whenever there is one exponent inside the bracket and one outside and the bracket has to be opened...In such a case the inner and outer exponents are multiplied. Giving us 2^6x+2

Next step compare 3 on the LHS with 3 on the RHS. Same with 2.
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by factor26 » Sat Jul 23, 2011 10:07 am
GREAT EXPLINATION!!

I TRIED TO SOLVE THE PROBLEM THE EXACT SAME WAY BUT WHEN I COMPLETED STEP 4 I WAS LOST! THANKS FOR THE HELP! KUDOS AND MANY THANKS!!
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by MBA.Aspirant » Sat Jul 23, 2011 10:51 am
factor26 wrote:IF X AND K ARE INTEGERS AND (12^X)(4^2X+1)=(2^K)(3^2), WHAT IS THE VALUE OF K?

(A) 5
(B) 7
(C) 10
(D) 12
(E) 14

OG ANSWER IS E ... CAN SOMEONE PLEASE BREAK DOWN THE CONCEPTS INVOLVED IN SOLVING THIS PROBLEM AND HOW TO SOLVE THIS PROBLEM?

THANKS!!


(12^X)(4^(2X+1))=(2^K)(3^2)

3^x * 2^2x * 2^(4x+2) = 2^K * 3^2

x =2

2^6x+2 = 2^k

k = (6*2) +2 = 14
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