ALGEBRA 2 6.0
CHAPTER 7 – EXPONENTIAL AND LOGARTIHMIC FUNCTIONS
WITH A CALCULATOR
You must be able to do the following:
 Sketch exponential functions of the form y  a  b xc  d , ( b  0, b  1 ) by identifying
transformations from the parent function, y  b x . Identify the domain, range,
asymptote and intercept(s) (if possible ).

Sketch logarithmic functions of the form y  a logb ( x  c)  d , (b  0, b  1) , by identifying
transformations from the parent function, y  logb x . Identify the domain, range,
asymptote and intercept(s) (if possible ).

Given appropriate data use the exponential regression feature of your calculator to
determine an exponential function. Use the function to determine the effective yield of
an investment or the inflation rate of the value of an item.

Identify the multiplier of a given exponential function and determine whether it models
growth ( > 1 ) or decay ( < 1 ).

Given the % of growth or decay, find the multiplier for an exponential function.

Solve exponential equations, (if possible, without logarithms), by using the fact that if
b x  b y then x  y , b  1.

Evaluate expressions involving log x , the common logarithm, knowing that log x implies a
base of ten. That is, log x  log10 x .

Evaluate expressions involving e , the natural base, knowing that e is an irrational number
(not a variable). e  2.71828... and log e x is abbreviated as ln x , the natural logarithm.
That is, ln 6  loge 6 .

Write exponential functions in logarithmic form and logarithmic functions in exponential
form.

Use the basic properties of logarithms (Product, Quotient, and Power) to simplify
logarithmic expressions and/or solve logarithmic equations, including those involving
common and natural logarithms.

Use the Exponential-Logarithmic Inverse Properties (logb b x  x, blogb x  x, ln e x  x,
and eln x  x) to simplify logarithmic expressions and/or solve logarithmic equations.

Use the One –to-One Property (logb x = logb y if and only if x  y) to simplify logarithmic
expressions and/or solve logarithmic equations, including those involving common and
natural logarithms.

Use Change of Base formula to evaluate logarithms with a base other than 10.

Solve exponential equations whose solutions require the use of the properties of
logarithms (such as 32 x1  5x or ex1 = 3x2 ).

Use the properties of logarithms to write logarithmic expressions involving more than one
term as a single logarithm and simplify, if possible.

Use the properties of logarithms to write a single logarithmic expression in expanded
form and simplify, if possible.

Solve logarithmic equations (if possible, without a calculator) by using the properties of
logarithms and putting the equations in exponential form. Be sure to check for any
extraneous solutions. The three basic types of logarithmic equations are
log 6 ( x  2)  log 6 (2 x)
log 6 ( x  2)  log 6 (2 x)  log 6 16
log 6 ( x  2)  log 6 (2 x)  1

Given a real life situation, write an exponential function to model the data and use the
function to make predictions.

Given a real life situation, model exponential growth or exponential decay by an equation
of the form y  aekt or y  ae kt and use logarithms to solve the problem.

 r
Given an appropriate real life situation, use a compound interest formula, A(t )  P 1  
 n
rt
or A(t )  Pe , to solve the problem.