SOLUTION: 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

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?
Solve log (small 3) (2x+1) = 2 for x.
Thanks a bunch!!
Theresa
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
log (small 3) (2x+1) = 2 for x.
That is log[3](2x+1) =2 ----(1) (here the base is 3)
This implies (2x+1) = 3^2
(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.
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
2x+1 = 9
2x = 9-1
2x = 8
x = 8/2 = 4
Answer: x = 4
Verification: Putting x = 4 in (1)
LHS = log[3](2x+1)
=log[3][2X4+1]
= log[3](9)
=log[3](3)^2
= 2Xlog[3](3) (using log[b](m)^n =nXlog[b](m) )
=2X1 [as log[3](3) = 1 (log of any posiitve quantity to the same base is 1) ]
=2 = RHS
Therefore our answer is correct

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