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# If 8^a+8^b=3^(b-2)*8^(a-1), a and b are positive integers, then what

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VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1014
WE: Supply Chain Management (Energy and Utilities)
If 8^a+8^b=3^(b-2)*8^(a-1), a and b are positive integers, then what  [#permalink]

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Updated on: 16 Aug 2018, 01:46
4
00:00

Difficulty:

85% (hard)

Question Stats:

32% (02:10) correct 68% (02:55) wrong based on 34 sessions

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If $$8^a+8^b=3^{b-2}*8^{a-1}$$, a and b are positive integers, then what is the product of a and b ?

A. 10
B. 12
C. 15
D. 18
E. 20

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PKN

Rise above the storm, you will find the sunshine

Originally posted by PKN on 15 Aug 2018, 22:37.
Last edited by Bunuel on 16 Aug 2018, 01:46, edited 1 time in total.
Renamed the topic.
Math Expert
Joined: 02 Aug 2009
Posts: 7971
Re: If 8^a+8^b=3^(b-2)*8^(a-1), a and b are positive integers, then what  [#permalink]

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15 Aug 2018, 22:58
PKN wrote:
If $$8^a+8^b=3^{b-2}*8^{a-1}$$, a and b are positive integers, then what is the product of a and b ?

A. 10
B. 12
C. 15
D. 18
E. 20

$$8^a+8^b=3^{b-2}*8^{a-1}.................8^b=3^{b-2}*8^{a-1}-8^a...............8^b=8^{a-1}(3^{b-2}-8)$$
so $$3^{b-2}-8$$ should be multiple of 8 or should be equal to 1
multiple of 8 with b as positive integer is not possible
so $$3^{b-2}-8=1.........3^{b-2}=8+1=9........3^{b-2}=3^2.....b=4$$
a -1 = b.....a= 4+1=5
ab=4*5=20

E
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Re: If 8^a+8^b=3^(b-2)*8^(a-1), a and b are positive integers, then what   [#permalink] 15 Aug 2018, 22:58
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