Question 30528
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