5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book May 8, 2018 13:46

Review of Precalculus 67

Properties of Exponents
Givena>0,b>0, andxandyare real numbers, then

ax·ay=ax+y

ax÷ay=ax−y

(ax)y=axy

(ab)x=ax·bx

(a

b

)x

=

ax

bx

Logarithmic function with basea:y=logaxif and only ifay=xwherex>0,a>0, and
a =1. (See Figure 5.3-24.)

(^0) (1, 0)
y = loga x, a > 1
x
y
0 (1, 0)
y = loga x, 0 < a < 1
x
y
Figure 5.3-24
Domain:{x|x > 0 }. Range:{all real numbers}.x-Intercept: (1, 0). Vertical asymptote:
y-axis. Behavior: strictly increasing.
Note thaty=logaxandy=axare inverse functions (that is, loga(ax)=alogax=x). (See
Figure 5.3-25.)
y
x
(0, 1)
(1, 0)
0
y = loga x, a > 1
y = ax, a > 1
y = x
Figure 5.3-25