How do you expand #log (10/y)#?

1 Answer
Mar 7, 2016

Answer:

#log10-logy#

Explanation:

The second law of logs says tha #logcolor(red)(x)-logcolor(blue)(y)# can be simplified to #log(color(red)(x)/color(blue)(y))#. The only requirement for this to work is that both #log#s must have the same bases.

For our problem of #log(10/y)#, we have to expand the expression. We need make sure that we end up with two #log#s with the same bases.

The first step is also the last step: take the numerator, and make that the first part of the expression, and make the denominator the second part. What I mean is this: #log(color(red)(10)/color(blue)(y))# becomes #logcolor(red)(10) color(orange)(-) logcolor(blue)(y)#. The #color(orange)(-)# is very important, because that is what differentiates division from multiplication.