Student Question

Which are the solutions of the equation lgx+lg(x-3)=1?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

lgx+ lg(x-3)=1

We know that:

logx+lgy= lgxy

and, log10=1

Now substitute;


==> x(x-3)=10

==> x^2-3x = 10

==> x^2 -3x -10=0

Now factorize:

==> (x-5)(x+2)=0

x1= 5

x2=-2 ( this solution is impossible because log-2 is undefined and x can not be a negative value)

Then the only solution is x1=5

To check:

lg5 + lg(5-3)= lg5+lg2 = lg10=1

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial