document.write( "Question 30528: I got this problem wrong on a test and rather than telling me what I did wrong, the teacher just wrote the answer as being X = 4. I have been going over it and I can't figure out this problem. Can someone please write this problem out for me so that I can hopefully figure this out?\r
\n" ); document.write( "\n" ); document.write( "Solve log (small 3) (2x+1) = 2 for x.\r
\n" ); document.write( "\n" ); document.write( "Thanks a bunch!!\r
\n" ); document.write( "\n" ); document.write( "Theresa \n" ); document.write( "
Algebra.Com's Answer #17155 by sdmmadam@yahoo.com(530)\"\" \"About 
You can put this solution on YOUR website!
log (small 3) (2x+1) = 2 for x. \r
\n" ); document.write( "\n" ); document.write( "That is log[3](2x+1) =2 ----(1) (here the base is 3)
\n" ); document.write( "This implies (2x+1) = 3^2
\n" ); document.write( "(using definition log[b](N) = p implies and is implied by N = b^p where Nis the number (strictly positive),b is the base and p is the power.
\n" ); document.write( "In words the definition goes like this:The logarithm of a positive number N to a given base b is the power p to which base b has to be raised to give the number N
\n" ); document.write( "2x+1 = 9
\n" ); document.write( "2x = 9-1
\n" ); document.write( "2x = 8
\n" ); document.write( "x = 8/2 = 4
\n" ); document.write( "Answer: x = 4
\n" ); document.write( "Verification: Putting x = 4 in (1)
\n" ); document.write( "LHS = log[3](2x+1)
\n" ); document.write( "=log[3][2X4+1]
\n" ); document.write( "= log[3](9)
\n" ); document.write( "=log[3](3)^2
\n" ); document.write( "= 2Xlog[3](3) (using log[b](m)^n =nXlog[b](m) )
\n" ); document.write( "=2X1 [as log[3](3) = 1 (log of any posiitve quantity to the same base is 1) ]
\n" ); document.write( "=2 = RHS
\n" ); document.write( "Therefore our answer is correct
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