Log/Exponential functions

Re Write Log

100

log₅25=2

5²=25

200

log₁₆256=2

16²=256

300

log₂₃1=0

23⁰=1

400

e^x-10= 50

x-10 = ln 50

500

64^1/2=8

log₆₄8=1/2

Exponential Functions

100

Which formula is used when compounding Continuously? 

A=Pe^rt

200

What is the y-intercept and is the function growing or decaying? 

y = (0.94)^t

y-intercept : (0,1)

Decaying : b<1

300

Regina invests $12,000 in an account that earns 3.5% annual interest, compounded continuously. What is the value of the account after 10 years? Round your answer to the nearest dollar.

$17,028.81

400

Tamira invests $6,000 in an account that pays 6% annual interest. How much will there be in the account after 3 years if the interest is compounded daily? 

$7,183.20

500

An investment grows according to the compounded continuous formula. After 7 years, the investment is worth $3,200 and is compounded continuously at an annual interest rate of 4%. What was the initial amount invested?

$2,418.51

Equation Rules

100

log₇10 - log₇3

log₇ 10/3

200

log₄(xy)

log₄x + log₄y

300

log₉a+log₉b+5log₉c

log₉(bac⁵)

400

log₃(z⁴x^1/2)

4log₃z + 1/2log₃x

500

log₇(x³y)⁴

12log₇x + 4log₇y

Solving Logs

100

2^x+2 = 5

0.3219

200

log₄ (x+7)=3

57

300

3 x 10^n-8 = 43

9.156

400

-9log₅ (-7x) = -18

x=-3.57

500

log (5m+7) = log (3m+9)

m = 1

Transformations

100

g(x)=2^x+5

left 5

200

f(x)= log (x-2)+1

right 2, up 1

300

r(x)=2log x + 2

vertical stretch by 2, up 2

400

Identify the vertical asymptote and domain of

 g(x)=log (x-3)+2

Asymptote : x=3

Domain: x>3

500

h(x)= -10^x+7-10

reflected over x - axis, vertical stretch by 5, left 7, down 10