Chapter 3:Exponential & Logarithmic Functions

Exponential Rules

100

The function denoted by f(x)=a^x

what is an exponential function/ exponential function f with base a?

200

exponential functions and logarithmic function are examples of ...

what are transcendental functions?

300

The exponential fool that Evaluate 

(x³)²

what is the natural base?

400

Identify they type of function, as shown below

f(x)= e^x

what is the natural exponential function?

Logarithmic rules

100

Write the equation that would be used to love the lograthmic equation 

 f(x)=log_ax

f(x)= log_a x

a^f(x) = x

200

the logarithmic function with base 10

what is the common logarithmic function?

300

the inverse of the function f(x) = e^x

what is the natural logarithmic function?

400

log_aa^x=x and a^loga(x)=x

what are inverse properties?

500

if log_ax = log_ay, then x=y.

what is the one-to-one property?

Properties of Logs

100

Condense the following, using the properties of logarithms

       6log₃ u + 6log₃ v

    log 3 (u⁶ v⁶)

200

condense the following using properties of logarithms:                   2 log 7

                     3

         log (7²)^1/3

300

Expand the following using properties of logarithms:               log ( t/c³)⁷

7 log t - 21 log c

400

condense the following using properties of logarithms: log_auⁿ

what is nlog_au?

500

condense the following using properties of natural logarithms: lnuⁿ

what is nlnu?

Solving logs and exponential functions

100

Solve the equation below

log (4k − 5) = log (2k − 1)

 log (4k − 5) = log (2k − 1)

              4k-5 = 2k -1

             4k-2k= -1+5

                   2k = 4

                     k = 2

200

Solve the equation below

3 ^{1 − 2x} = 243

3 ^{1 − 2x} = 243

3 ^{1 − 2x} =3⁵

1 - 2x = 5

1 - 5 = 2x

-4 = 2x

-2 = x

300

What is the value of x if 

e^lnx=e³ 

e^lnx = e³

lnx = 3

x = e³

x= 20.086

400

Solve the equation. Round your answers to the nearest ten-thousandth.

6e ^{5x − 6} − 4 = 50

       6e ^{5x − 6} − 4 = 50

        6e ^{5x − 6}= 54

         e ^{5x − 6} = 9

        5x - 6= ln(9)

         x = (2.1972+6) / 5

         x = 1.6394

500

Is the following a true statement based on the rule for solving exponential equations?

a^x=a^y if and only if x=y

True statement

Application questions

100

The total  gallon of Orange juice each person consumes yearly has decreased 4.1% each year. In 1981 each person drank 16.5 gallons of orange Juice on average. What was the approximate amount consumed in 2010

  y = a.b^x

  y = 16.5 ( 1 - 0.04)²⁹

  y = 5.1 

5.1 gallons of juice consumed per person

200

You buy a car for $7500 that depreciated at a rate of 15% a year. 

a) How much is the car worth after 4 years?

b) When will the car be worth  $2500 or less

  y = a.b^x

  y = $7500(1- 0.15)⁴

  y =$3915. 05

  $2500 = $7500 (1 - 0.15)^t 

   log (2500/7500) = T log(0.85)  

    T = 7 years

300

Mary invested $5000 into an account that earns 8% interest compounded daily. After 12 years What is the amount in the account?

A= P( 1+ (r/n))^n(t)

A= $5000 (1+ (0.08/365))^12(365)

A= $13057.11

400

When Jacob was born $18000 was invested in his trust fund at a rate of 6.25% interest, compounded continuously.

a) What was the balance in Jacob's account at age 15?

b) How old will Jacob be when his investment reaches $75000

   A =Pe^rt

    A =18000.e ^{0.0625 (15)}

   A = $45964. 61

b) $75000 = $18000 .e ^{0.0625 (t)}

      ln ($75000/$18000) = 0.0625 t

      ln (1.4271) / 0.0625 = t

         T = 23 years (approximately)

500

A population of 3000 people doubles in size every 10 years. What is the population size after 50 years?

   y =a.b^x

   y = 3000(2)⁵

   y = 96000

96000 people after 50 years.