document.write( "Question 29618: I need help finding the solution(s) to log(5x-3)-log(x-1)=1 \n" ); document.write( "
Algebra.Com's Answer #16428 by sdmmadam@yahoo.com(530)\"\" \"About 
You can put this solution on YOUR website!
log(5x-3)-log(x-1)=1 ----(1)
\n" ); document.write( "log[(5x-3)/(x-1)]=1 (using log(a)-log(b) = log(a/b) the common base being 10)
\n" ); document.write( "[(5x-3)/(x-1)]= (10)^1
\n" ); document.write( "(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 )
\n" ); document.write( "That is [(5x-3)/(x-1)]= (10)
\n" ); document.write( "Multiplying by (x-1) through out
\n" ); document.write( "(5x-3)=10X(x-1)
\n" ); document.write( "5x-3 = 10x-10
\n" ); document.write( "-3+10 = 10x-5x (grouping like terms,changing sign while changing side)
\n" ); document.write( "7 = 5x
\n" ); document.write( "That is 5x =7
\n" ); document.write( "Dividing by 5
\n" ); document.write( "x = 7/5
\n" ); document.write( "Answer: x = 7/5
\n" ); document.write( "Verification: x = 7/5 in (1)
\n" ); document.write( "LHS = log(5x-3)-log(x-1)
\n" ); document.write( "=log(7-3)-log(7/5-1)
\n" ); document.write( "=log(4)-log[(7-5)/5]
\n" ); document.write( "=log(4)-log(2/5)
\n" ); document.write( "=log[4/(2/5)]
\n" ); document.write( "=log[4X5/2]
\n" ); document.write( "=log(10)
\n" ); document.write( "=1 (since log(10) to the same base 10 is =1)
\n" ); document.write( "=RHS\r
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