Exponential and Logarithmic Functions Practice I

e

the base of natural exponential and logarithmic functions

exponent

a number which indicates how many times a base is multiplied by itself

Label this image

A - base
B - index

a^m x aⁿ

a^m+n

a^m/aⁿ

a^m-n

a⁰

1

(a^m)ⁿ

a^mn

a^(1/m)

m√a

a^(m/n)

(a^m)^(1/n) or (a^1/n)^m or n√a^m or (n√a)^m

Describe the properties of the graphs y = a^x and y = e^x, a>1

• The domain is x∈R and the range is y>0

• The graph does not cut the x-axis

• The line y = 0 is a horizontal asymptote as x→∞

• The graph of y is smooth and continuous

• The graph is an increasing 1-1 function

Describe the graph of y = a^x, 0<a<1

• The domain of a^x is x∈R and the range is y>0

• The graph does not cut the x-axis

• The line y = 0 is a horizontal asymptote as x→∞

• The graph of y is smooth and continuous

• The graph is a decreasing 1-1 function

logarithm

the power a base has to be raised to in order to produce a certain number — the argument

Label this diagram

A - exponent
B - base
C - argument

ln x

the natural logarithm of x

log

logarithm of x

log_aa/ln e

1

log_a1/ln 1

0

log_a(xy)/ln(xy)

log_ax + log_ay/ln x + ln y

log_axⁿ/ln xⁿ

nlog_ax/nln x

change of base formula (b→a)

log_ax = (log_bx/log_ba)