Evaluate the following exponential functions
given the value for x
Y = 3(1/2)x (x = 2)
Y = 2(4)x (x = 3)
Y = ½(4)x (x = -3)
y = bx
Then…
logb y = x
A
= Pert
 A = amount in account
 P = principal (starting amount)
 r = annual interest rate
 t = time in years




Evaluate the continuously compounded
interest formula for the given information
P = 5000
4000
r = 4%
5%
t = 15 years
10 years

Suppose you invest $1050 at an annual
interest rate of 5.5% compounded
continuously. How much will you have in the
account after 5 years?
How many years will
it take for you to save $3000?

A culture of bacteria starts with 500 and
doubles every 15 minutes. Find a model for
this relationship. (hint: solve for r)

Log8 16 = x
log927 = x

Log2 32 = x
log381 = x

Log(3x + 1) = 5
log(7 – 2x) = -1

Log2 (2x – 2) = 4
log2 (3x – 4) = 3

Log (3x + 1) = 2

log2 (3x – 4) = log2 (2x + 6)

Log4 64 = x
log9 3 = x

2x = 8
3x = 27
Product property
 Logb M + logb N = logb MN


Log5 2 + log5 6 = log5 12

Log4 5 + log4 3 =

Log 7 + log 2

Log3 4 + log3 5
log7 12 + log7 3
ln 7 + ln 3

Quotient property
𝑀
logb
𝑁

Logb M - logb N =

Log5 6 - log5 2 = log5 3

Log4 12 - log4 3 =

Log 7 - log 2 =

Log3 3 - log3 9 =
log7 12 – log7 3
ln 9 - ln 3 =
Power property
 X logb M = logb Mx


3 log2 5 = log2 53

2 log4 4 =
3
log2 2 =
4 ln 5 =
2
log8 4 =
2 log3 3

Log 7 + log 2

5 log 3 + log 4
log2 9 – log2 3
log7 6 + log7 2 – log7 3
 Log
x – log 6 = log 15
 Log4
(x2 – 9) + log4 9 = 0
 Log3
 Ln
(x2 + 8) – log3 4 = 3
(x + 7) + ln (x +3) = ln 77
 Log3
3x3
 Log5
xy3z2
 Ln
𝑦3
𝑥
 Log9
(3xz)2

Growth factor
◦ B>1

examples: 2, 3, 7,10
Decay factor
◦ B<1
examples: ½, ¾, 1/6
y = bx
Then…
logb y = x