Cracking The Ap Calculus ab Exam 2018

When you raise an expression to the power of zero, you get one.

x^0     =   1

When you raise an expression to the power of one, you get the expression.

x^1     =   x

When you raise an expression to a negative power, you get the reciprocal of the expression to the absolute
value of the power.

Logarithms

A logarithm is the power to which you raise a base, in order to get a value. In other words, logbx = a

means that ba = x. There are several rules of logarithms that you should be familiar with.

When you take the logarithm of the product of two expressions, you add the logarithms.

log(ab) =   log a   +   log b

When you take the logarithm of the quotient of two expressions, you subtract the logarithms.

log     =   log a   −   log b

When you take the logarithm of an expression to a power, you multiply the logarithm by the power.

log(ab) =   b   log a

The logarithm of 1 is zero.

log 1   =   0

The logarithm of its base is 1.

logb b  =   1

You cannot take the logarithm of zero or of a negative number.

In calculus, and virtually all mathematics beyond calculus, you will work with natural logarithms. These