Exponentials & Logarithms - Cool math Algebra Help Lessons

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Coolmath Algebra
Exponentials & Logarithms Lesson 15 - Solving Logarithmic Equations
(page 5 of 7)
---- This algebra lesson explains how to solve log (logarithmic) equations

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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!

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:

Solve

Continued on the next page

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