Indices question!

Apr 2010
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Given that \(\displaystyle 10^{2n} \times 5^{4-3n} = 2^x \times 5^y\), express y in terms of n.

Answer: \(\displaystyle x = 2n\), \(\displaystyle y = 4 - n\)
I don't know how to begin, how do I get two answers from one given expression? Sorry if I sound dumb but any help will be greatly appreciated! Thanks in advance.
 

skeeter

MHF Helper
Jun 2008
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\(\displaystyle 10^{2n} \cdot 5^{4-3n} = 2^x \cdot 5^y\)

\(\displaystyle (2 \cdot 5)^{2n} \cdot 5^{4-3n} = 2^x \cdot 5^y\)

\(\displaystyle 2^{2n} \cdot 5^{2n} \cdot 5^{4-3n} = 2^x \cdot 5^y\)

\(\displaystyle 2^{2n} \cdot 5^{4-n} = 2^x \cdot 5^y\)

finish up by equating exponents
 
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Apr 2010
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Oh thank you very much skeeter! I haven't really done this sort of sum for a while so I completely forgot about that. Oops.
 

HallsofIvy

MHF Helper
Apr 2005
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Note that is m and n could be any numbers, there would be an infinite number of solutions. This problem is assuming that m and n are positive integers.
 
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Jul 2010
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Hi im stuck on a question, anyone can help?
simplify
9^-1/2 x 8^2/3
 
Jan 2010
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(Removed as author of post #5 started a new thread.)