${\mathit{log}}_b\left(x\right)$

Base Case: ${\mathit{log}}_b\mathrm{(}x\mathrm{)}$

Note :

–          This is base special case for any logarithm with a log base b .

–          It is the more general case of the $\mathit{ln}\left(x\right)$special case.

–          Keep in mind that as soon as whatever is inside the function, inside the parenthesis, is more than just your basic x , the problem’s primary rule becomes a chain rule. Whatever you replace the x with inside your base special case will become the inside piece of your chain rule.

–          Also, when you apply the chain rule, everywhere you see an x in the $f\prime \left(x\right)$ equations above, you will plug in the full inside piece.

–          You will need to know this table equally as well in both directions, left to right and right to left.