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If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k? [#permalink]
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14 Jun 2015, 04:59
2
3^k+3^k=(3^9)^3^9 - 3^k --> moving the - 3^k to the other side: 3(3^k) = (3^9)^3^9 --> using the properties of powers, we are now adding the exponents: 3^k+1 = 3^ (3^2)^(3^9) (here we broke 9 into 3^2) k+1 = 3^2*3^9 k+1 = 3^11 k = 3^11 - 1.
The common term in this problem is the recurring base of 3. We will group like terms (i.e. all the terms with k on the left side, all the other powers of 3 on the right side), then simplify each power of 3 using exponent rules.
Re: If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k? [#permalink]
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17 Feb 2016, 22:49
(3^9)^3^9= 3^(3^2*3^9)=3^11 now taking all k terms on one side 3^k+3^k+3^k = 3^(k+1) comparing power as bases are same we get k+1=3^11, k=3^11-1 E answer'
If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k? [#permalink]
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18 Feb 2016, 04:32
Anyone knows what is the maximum number of "aggregated exponents" GMAT is likely to test? I could only solve this question because it regarded only "2 aggregated powers":\((3^9)^{3^9}\). Does "3 aggregated powers" such as \({3^9}^{3^9}\) are possible to appear on GMAT questions? How to solve them?
Re: If 3^k + 3^k = (3^9)^3^9 – 3^k, then what is the value of k? [#permalink]
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05 Apr 2018, 12:19
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