log (5x-1) - log (X-2) = log 3   solve for x

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log (5x-1) - log (x-2) = log 3

First we will simplify the equation:

We know that:

log a = log b = log a/b

==> log (5x-1)/(x-2) = log 3

Also, we know that:

if log a = log b ==> a = b

==> (5x-1) /(x-2) = 3

Now multiply by (x-2):

==> (5x-1) = 3(x-2)

==> 5x-1 = 3x - 6

Combine like terms:

==> 5x-3x = -6 + 1

==> 2x = -5

==. X= -5/2

But the function is not defined when x= -5/2

==> There is no solution.

Approved by eNotes Editorial Team

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