Log Properties Flashcards Preview

Algebra 2 + Trig > Log Properties > Flashcards

Flashcards in Log Properties Deck (23):
1

Natural base e

y=e^x exponential function
y=e^-x (inverse)

2

f(x) = b^x vs f(x) = e^x

Growth: b > 0 vs x >0
Decay: 0

3

Which 2 functions are the same?
y=2^x
y=2^-x
y=(1/2)^x

y=2^-x
y=(1/2)^x
Bc y=2^-x -- 1/2^x -- (1/2)^x

4

Natural Base Functions
y=ae^rx

Growth / decay depends on whether the x is negative or positive

5

Continuously compounded interest

A =Pe^rt
y=5e^0.25x -- growth
y=0.8e^-3x -- decay

6

An exponential function is the inverse of a logarithmic function

f(x)=b^x --- g(x)=log_b_ x

(_b_ means subscript b)

7

b^x=m ---

log_b_m = x
Ex: 2^x = 8 --- log_2_ 8 = 3

8

y=2^x and x=2^y are

Inverses

9

x=2^y and y=log_2_x are

The same thing

10

Common log

y=logX
(base 10)

11

Exponential vs Logarithmic graph

Exponential:
g(x)=b^x, (0,1), asymptote = x-axis, domain: all reals, range: y>0
Logarithmic:
g(x)=log_b_x, (1,0), asymptote = y-axis, domain: x>0, range: all reals

12

log_b_Y=x if

b^x=Y

13

Base cancellation

common bases cancel out
lne^x^3 --- log_e_e^x^3 (both e's cancel out) =x^3

14

ln = natural log

ln = log_e_
log_e_X = lnX

15

log_b_mn =

log_b_m + log_b_n

16

log_b_ m/n =

log_b_m - log_b_n

17

log_b_m^n =

nlog_b_m

18

log_b_b =

1

19

log_b_1 =

0

20

logX =

log_10_X

21

lne^2 + lne^5 =

*common base*
ln(e^2 * e^5)
log_e_e^7
=7

22

log_3_7 =

log7 / log3 = ln7 / ln3

23

x=log_e_(y-4) ---

e^x = y-4