Question 29618: I need help finding the solution(s) to log(5x-3)-log(x-1)=1
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! log(5x-3)-log(x-1)=1 ----(1)
log[(5x-3)/(x-1)]=1 (using log(a)-log(b) = log(a/b) the common base being 10)
[(5x-3)/(x-1)]= (10)^1
(using log(N) to base b = the powerp implies and is implied by N =(b)^p where N is a strictly positive number and here N= [(5x-3)/(x-1)], b= 10 and p = 1 )
That is [(5x-3)/(x-1)]= (10)
Multiplying by (x-1) through out
(5x-3)=10X(x-1)
5x-3 = 10x-10
-3+10 = 10x-5x (grouping like terms,changing sign while changing side)
7 = 5x
That is 5x =7
Dividing by 5
x = 7/5
Answer: x = 7/5
Verification: x = 7/5 in (1)
LHS = log(5x-3)-log(x-1)
=log(7-3)-log(7/5-1)
=log(4)-log[(7-5)/5]
=log(4)-log(2/5)
=log[4/(2/5)]
=log[4X5/2]
=log(10)
=1 (since log(10) to the same base 10 is =1)
=RHS
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