SOLUTION: 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)

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Question 295203: 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:
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(17219) (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