This is an area where drilling can make a huge difference. That’s for two reasons:
Are you facile enough with exponents and logarithms to do great on the AMC?
In order to answer “yes,” you should know or have all of the following, without any hints or prompting:
This means that you should be able to algebraically combine and manipulate exponents and logarithms without having to stop and think for very long in the middle of the process. In addition, you should be able to see at least two or three different possible approaches for any problem involving logarithms or exponents in a significant way.
For logarithms, they are as follows:
$g_{b}c=ANSWER⟷b_{ANSWER}=c$
$gx+g y=gxy$
$gx−g y=gyx $
$ga_{b}=g(a_{b})=bg a$
$g_{b}a=log bloga $
$lnx=g_{e} x$
$g a=gb⟷a=b$
For exponents, they are as follows:
$x_{a}x_{b}=x_{a+b}$
$x_{b}x_{a} =x_{a−b}$
$(xy)_{a}=x_{a}y_{a}$
$(x_{a})_{b}=x_{ab}=(x_{b})_{a}$
$(yx )_{a}=y_{a}x_{a} $
$x_{−n}=x_{n}1 $
$x_{nm}=nx_{m} =(nx )_{m}$
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