Hey, you know...  We'd better start checking our answers to make sure they're OK!

Check
x = 3:

Log( x^( 2 ) - x ) = Log( 6 )  ...  Log ( 3^( 2 ) - 3 ) = Log( 6 )  ...  Log( 6 ) = Log( 6 )  ...  Yep!

 

Check
x = -2:
Log( x^( 2 ) - x ) = Log( 6 )  ...  Log( ( -2 )^( 2 ) - ( -2 ) ) = Log( 6 )  ...  Log( 4 + 2 ) = Log( 6 )  ...  Yep!

So, in this case, our answers are both good.

 

One thing you always need to watch out for is an answer that breaks a log's biggest rule:

You can't take the log of a negative number!

Why not?

Look again at the log's graph:

Logarithms only exist
in positive
x values!

So, Log 0 doesn't exist!

Log (-5) doesn't exist!

graph of Log

Teachers love sneaking these guys in for answers...  So, keep an eye out!

Watch out for x's that give Log 0, too!
 


YOUR TURN:

SolveLn( x^( 2 ) - 10 ) = Ln( 3x )