Logarithm Problem

Date: 9/15/95 at 12:50:10
From: Anonymous
Subject: Logarithm Help

Dear Dr. Math 

We are students in the North River School Advanced Math class. We have 
finally found a problem that none of us can figure out.  We were 
wondering if your math team could possibly help us?

Here it is......

2log(base 5) (3a+1) = log(base 5) 4 - 2log(base 5) (2a-1)

???????????????????????? HELP  ????????????????????????????

Our book has an answer of 3, but we still can't figure out how they got it;
the book may be wrong but we would like to know for sure.

Thank you so much for your time
    Students
    Nova lotus, Kristi, Bridgit.            

Date: 9/15/95 at 18:53:44
From: Doctor Steve
Subject: Re: Logarithm Help

Hello folks,

Sorry to not have time at the moment for a thorough look
but it seems clear that 3 can't be right since that would
give a negative number on the right side of the equation
and a positive number bigger than 2 on the left.  Do you
see why we can say that just looking at it?

It seems to us that you get the answer by solving:

6a^2 - a - 3 =0

Can you figure out where we got that equation?

Write back with more questions if you have them or if you figure
any mistakes we made.

-- Doctor Steve,  The Geometry Forum