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If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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08 Jun 2015, 08:58
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If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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08 Jun 2015, 09:20
Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4
Kudos for a correct solution. \(3^a + 3^{a  2} =3^{a2}(3^2+1)=3^{a2}*10\) \((90)(3^b)=3^2*10*3^b=3^{b+2}*10\) so \(3^{a2}*10=3^{b+2}*10\) \(b+2=a2\) > \(b = a4\) Answer is A
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If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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08 Jun 2015, 09:58
Ans is A Please find the solution below in file attached.
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Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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08 Jun 2015, 11:00
If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? Lets take a=2. 3^2+3^0=(90)3^b > 10/90=3^b > 3^2=3^b > b=2. Substitute a=2 in answer choices, only A fits correctly. Thanks, Please give me kudos.
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Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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09 Jun 2015, 01:48
Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4 Ans : A Solution: generalizing both sides gives us 3^a2 * 5*2 = 3^ b+2 * 5*2 means a2=b+2 b= a4
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Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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10 Jun 2015, 02:15
If \(3^a + 3^{(a  2)} = (90)(3^b)\), what is b in terms of a?
\(3^a + 3^{(a  2)} = (3^2*10)(3^b)\) > \(3^a(1 + 3^{(2)}) = (3^{(2+b)})(10)\) > \(3^a\frac{10}{9} = (3^{(2+b)})(10)\)> \(3^a = (3^{(2+b)})(9)\)> \(3^a = (3^{(2+b)})(3^2)\)> \(3^a = (3^{(4+b)})\)> \(a=4+b\)> \(b=a4\) or A



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Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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14 Jun 2015, 04:42
3^(a2) X (5*2) = 3^ (b+2) X (5*2) a2=b+2 b= a4 Ans A



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If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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17 Jun 2015, 04:18
Harley1980 wrote: Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4
Kudos for a correct solution. \(3^a + 3^{a  2} =3^{a2} (3^2+1)=3^{a2}*10\) \((90)(3^b)=3^2*10*3^b=3^{b+2}*10\) so \(3^{a2}*10=3^{b+2}*10\) \(b+2=a2\) > \(b = a4\) Answer is A Hello could you explain the part in red to me plz? I understand that you took 3^a2 as a common factor. But how did you get that taking the power of "a2" from a power of "a" leaves a square?



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Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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17 Jun 2015, 04:28
pacifist85 wrote: Harley1980 wrote: Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4
Kudos for a correct solution. \(3^a + 3^{a  2} =3^{a2} (3^2+1)=3^{a2}*10\) \((90)(3^b)=3^2*10*3^b=3^{b+2}*10\) so \(3^{a2}*10=3^{b+2}*10\) \(b+2=a2\) > \(b = a4\) Answer is A Hello could you explain the part in red to me plz? I understand that you took 3^a2 as a common factor. But how did you get that taking the power of "a2" from a power of "a" leaves a square? Hello pacifist85If you multiply \(3^{a2}\) on \(3^2\) you receive \(3^{(a2)+2}\) > \(3^a\)
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Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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17 Jun 2015, 04:55
Oh ok I think i see it now. So, you basally want to take 3^a2 out, as a common factor. You have 3^a, and from that power (a) you are subtracting a2, as you have already taken this as a fator.
Then you would have 3^a(a2) = 3^aa+2 = 3^2. I hope I got it right...



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If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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17 Jun 2015, 05:04
pacifist85 wrote: Harley1980 wrote: Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4
Kudos for a correct solution. \(3^a + 3^{a  2} =3^{a2} (3^2+1)=3^{a2}*10\) \((90)(3^b)=3^2*10*3^b=3^{b+2}*10\) so \(3^{a2}*10=3^{b+2}*10\) \(b+2=a2\) > \(b = a4\) Answer is A Hello could you explain the part in red to me plz? I understand that you took 3^a2 as a common factor. But how did you get that taking the power of "a2" from a power of "a" leaves a square? Hi pacifist, Just for your information and better understanding here are Rules of exponents The powers of the numbers add up for the same base when the numbers are multiplied i.e. \(a^x * a^y = a^{(x+y)}\)
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Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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01 Jul 2015, 15:27
Harley1980 wrote: Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4
Kudos for a correct solution. \(3^a + 3^{a  2} =3^{a2}(3^2+1)=3^{a2}*10\) \((90)(3^b)=3^2*10*3^b=3^{b+2}*10\) so \(3^{a2}*10=3^{b+2}*10\) \(b+2=a2\) > \(b = a4\) Answer is A I am confused on the first step you took that factored out the \((3^2+1)\)



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If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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01 Jul 2015, 17:29
xLUCAJx wrote: Harley1980 wrote: Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4
Kudos for a correct solution. \(3^a + 3^{a  2} =3^{a2}(3^2+1)=3^{a2}*10\) \((90)(3^b)=3^2*10*3^b=3^{b+2}*10\) so \(3^{a2}*10=3^{b+2}*10\) \(b+2=a2\) > \(b = a4\) Answer is A I am confused on the first step you took that factored out the \((3^2+1)\) Hi xLUCAJx, They factored out the whole expression, \(3^{a2}\), so that the \((3^{2}+1)\), or \(10\), would be isolated. Thinking forward, not one but two steps ahead, and it saved them from a fraction.



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Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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01 Jul 2015, 17:44
xLUCAJx wrote: Harley1980 wrote: Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4
Kudos for a correct solution. \(3^a + 3^{a  2} =3^{a2}(3^2+1)=3^{a2}*10\) \((90)(3^b)=3^2*10*3^b=3^{b+2}*10\) so \(3^{a2}*10=3^{b+2}*10\) \(b+2=a2\) > \(b = a4\) Answer is A I am confused on the first step you took that factored out the \((3^2+1)\) Think of it in this way: \(3^a+ 3^{a  2} =3^{a+22}+3^{a2}=3^{a2}*3^{2}+ 3^{a2} = 3^{a2}(3^2+1)=3^{a2}*10\) Going from 1st part to the second, we added and subtracted 2 from a as we need the power of a2 common. For the second part, we used the property \(a^{x+y} = a^x*a^y\), where x= a2 and y = 2. I hope this clears your doubt.



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Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
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21 Jun 2018, 16:58
Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4 Simplifying, we have: 3^a + 3^a x 3^2 = (90)(3^b) 3^a(1 + 3^2) = 90(3^b) 3^a(1 + 1/9) = 90(3^b) 3^a(10/9) = 90(3^b) 3^a = 90(3^b) x 9/10 3^a = 9 x 3^b x 9 3^a = 81 x 3^b 3^a = 3^4 x 3^b 3^a = 3^(4 + b) a = 4 + b a  4 = b Answer: A
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