# log 2x + log 5 = log (4x+2)

You may approach different methods to solve this equation, hence, either you may convert the sum into a product, or you move the terms that contain x to the left side and the constant term to the right.

Converting the sum in a product yields:

Hence, substituting for yields:

Equating...

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You may approach different methods to solve this equation, hence, either you may convert the sum into a product, or you move the terms that contain x to the left side and the constant term to the right.

Converting the sum in a product yields:

Hence, substituting for yields:

Equating the numbers yields:

Hence, evaluating the solution to the given equation yields

Approved by eNotes Editorial Team

log 2x + log 5 = log (4x + 2)

We know that:

log a + log b = log a*b

==> log 2x*5 = log (4x+2)

==> log 10x = log (4x+2)

==> 10 x = 4x + 2

==> 6x = 2

==> x= 2/6 = 1/3

==> x= 1/3

Approved by eNotes Editorial Team