Check for Extraneous Solutions

My class is having a hard time understanding how to do these because we don't understand the Inverse Property solution in the problem

and example problem we are having trouble with is:

Log base[2](x-6)=3+log base[2](x-1)

A solution to this problem and extra advice would be nice.

Re: Check for Extraneous Solutions

Quote:

Originally Posted by

**paigesisco** My class is having a hard time understanding how to do these because we don't understand the Inverse Property solution in the problem

and example problem we are having trouble with is:

Log base[2](x-6)=3+log base[2](x-1)

Re: Check for Extraneous Solutions

And then to check for extraneous solutions: plug your x value back into the original equation (which of course we all do every time anyway <grin>). If you'd wind up taking the log of a negative number, then that solution doesn't work and is an extraneous solution.

Re: Check for Extraneous Solutions

Hello, paigesisco!

Note that the domain of the solution is:

. . Also that:

We have: .

. . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . . .

But this is not in the domain.

It is an extraneous root.