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Algebra: Exponents and operations on exponents

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Click here to see ALL problems on Exponents Question 295203: I found this question in book entitled 1001 solved problems in engineering math, the book already gives the answ er but i dont understand how it is done,here is the question: (a^n)(a^m)=100000 (a^n)/(a^m)=10 find the value of a: I hope it will be answered with some explanation in it. thank you for the help. Found 2 solutions by richwmiller, dabanfield:

Answer by richwmiller(16928) (Show Source): You can put this solution on YOUR website! http://www.hostebook.com/Products/153-1001-solved-problems-in-engineering-mathematics-free-download.aspx

Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website! I found this question in book entitled 1001 solved problems in engineering math, the book already gives the answer but i dont understand how it is done,here is the question: (a^n)(a^m)=100000 (a^n)/(a^m)=10 find the value of a: a^n*a^m = 100000 a^(n+m) = 100000 log a^(n+m) = log 10^5 (n+m)*log a = 5 1.) n*log a + m*log a = 5 a^n/a^m = 1 a^(n-m) = 10^1 log a^(n-m) = log 10^1 (n-m)*log a = 1 2.) n*log a - m*log a = 1 Adding 1.) and 2.) we have: 2*n*log a = 6 n*log a = 3 n = 3/log a Substituting 3/log a for n in 2.): ((3/log a)*log a) - m*log a = 1 3 - m*log a = 1 m*log a = 2 m = 2/log a Since a*(n-m) = 10 (n-m)*log a = 1 log a = 1/(n-m) log a = 1/((3/log a - 2/log a)) log a = 1/log a (log a)^2 = 1 log a = +sqrt(1) or -sqrt(1) log a = 1 or log a = -1 By definition of a log then: a = 10 or a = 1/10

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