Unit 5 Log & Exponent Formulas/Rules

Question 1

general form of an exponential function

Answer 1

Ca^x

Question 2

law of exponents #1: b^x x b^y

Answer 2

b^x+y

Question 3

law of exponents #2:
(ab)^x

Answer 3

a^xb^x

Question 4

law of exponents #3:
b^x/b^y

Answer 4

b^x-y

Question 5

law of exponents #4:
(a/b)^x

Answer 5

a^x/b^x

Question 6

law of exponents #5:
b⁰

Answer 6

1
* b does not equal zero

Question 7

law of exponents #6:
b^x=b^y

Answer 7

x=y

Question 8

law of exponents #7:
a^x=b^x

Answer 8

a=b

Question 9

law of exponents #8:
(b^x)^y

Answer 9

b^xy

Question 10

law of exponents #9:
a^-x

Answer 10

1/a^x

Question 11

how to tell if it’s linear

Answer 11

the average rate of change is constant

Question 12

how to tell if it’s exponential

Answer 12

the ratio of consecutive outputs are constant (& average rate of change is not constant)

ex. f(0)/f(-1)=1/2, f(1)/f(0)=1/2, f(2)/f(1)=1/2

Question 13

logarithm to base b: if b^y=x then….

Answer 13

log_bx=y

Question 14

common log (base 10): if 10^y=x, then….

Answer 14

log₁₀x=(log x=y)

Question 15

natural log (base e): if e^y=x, then…

Answer 15

log_ex=(ln x=y)

Question 16

properties of logarithms #1:

if log_a1=0 then….

Answer 16

a⁰=1 ALWAYS

Question 17

properties of logarithms #2:
log_aa=?

Answer 17

log_aa=1

a=a

Question 18

properties of logarithms #3:
log_aa^x=?

Answer 18

log_aa^x=x

a’s cancel out so it’s x=x

Question 19

properties of logarithms #4:
a^log_ax=?

Answer 19

a^log_ax=x

cancels out where x=x

Question 20

properties of natural logs #1:
ln 1=?

Answer 20

ln 1=0

Question 21

properties of natural logs #2:
ln e=?

Answer 21

ln e=1

Question 22

properties of natural logs #3:
ln e^x=?

Answer 22

ln e^x=x

Question 23

properties of natural logs #4:
e^{ln x}=?

Answer 23

e^{ln x}=x

Question 24

when expanding…….properties of logs law #1:

log_b(MN)=?

argument: multiply=add

Answer 24

log_bM + log_bN

Question 25

when expanding….properties of logs law #2:
log_b(M/N)=?

Answer 25

log_bM-log_bN

Question 26

properties of logs law #3:
log_bN=log_bM
then…..

Answer 26

M=N

Question 27

when expanding/simplifying……properties of logs law #4:
log _bM^k=?

Answer 27

k(log_bM)

Question 28

change of base formula

Answer 28

log_bx=(log_ax)/(log_ab)

Question 29

how to check for extraneous solutions with logs

Answer 29

1. argument is greater than zero
2. base is greater than zero
3. base does not equal 1