Logarithms: a simple trick to avoid tricks

Most  my Algebra 3 students are taking the class because they were too weak to move onto a rigorous 4th year of high school math. They struggled with Algebra 2.  For that reason, I consider them to be a good testing ground for pedagogical strategies.  Such is the case with logarithms. Textbook instructions typically look like this and are often accompanied by pictures with arrows to help students follow the memorized path.

To change from exponential form to logarithmic form, identify the base of the exponential equation  and move the base to the other side of the equal sign and add the word “log”. Do not move anything  but the base, the other numbers or variables will not change sides.

circle

Rather than have them memorize that, and then have them memorize how to reverse, my students learn to understand the definition of a log, “A log is an exponent.”  Whenever I say “base”, I speak an octave lower, relating sound to subscript.

1)  Read:   log base 2 of 8 is an exponent
2) Write:   “What exponent, on a base 2 produces an 8?”
3)  Write:  2 x =8

The trick that avoids the tricks (going around in a circle or whatever) is to have them write as in step 2.  By writing, they must read and interpret.  By reading and interpreting they make sense out of and remember what all the parts mean.  An exponent is an exponent and a base is a base.  Unfortunately I can’t find a definition for what we take a log of, so we call it “the box.”

box

It does help to clown up the “base” in a deep voice:  that’s Anchor Theory.  But the silver bullet seems to be writing to solidify association. With that strong association, my students practically coast through the rest of the unit. Writing has long been known to as a best practice for study skills.  Writing even seems to surpass keyboarding.  So it makes sense that writing the associations between exponentials and logarithms will yield the results I am observing with my own students.  The hardest part is for me to have the will-power to insist my students write.  I like to be the laid-back nice lady; but I work hard to convince my students they will love their test scores if they will put forth the effort.  By the time my classes get to logarithms, they trust me.

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