Question 759176
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Find the exact value solution 

log (5x) + log (x-1) = 2
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x = 5 or  -  4, as stated by the other person, is partly WRONG!   

log (5x) + log (x - 1) = 2
Looking at the logarithmic equation, the smaller log argument, x  -  1 MUST be > 0.
So, x  -  1 > 0, and therefore, x > 1. 

We then have: log (5x) + log (x - 1) = 2, with x > 1

So, x = 5 is the ONLY solution, as x = - 4 is EXTRANEOUS.</font></font></font></b></pre>