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Log Graphs

100

y = log (x+3) -5

What is the range? 

All real numbers

200

y = log (x-7) +3

Name the base, and the transformations

base:10

right 7, up 3

300

y = -3 ln (x+2) -1

Name the base, and list the transformations

Base: e

Transformations: left 2, down 1

400

y = log (x-2) +4

Name the asymptote and the domain

Asymptote:  x = 2

Domain: (2, infinity)

500

y = - log (x+1) -5

Name the asymptote and the domain

Asymptote: x= -1

Domain: (- infinity, -1)

Natural Log

100

3 ln (x) = 12

x = e⁴

200

2 ln (x -5) = 16

x= e⁸+5

300

4 ln (x+2) = 16

x =e⁴-2

400

5 ln (2x) = 10

x = e²/2

500

4 ln (5x-1) =20

x = (e⁵+1)/5

Solving

100

log₂(x) = 4 

x= 16

200

log_x64 = 6

x =2

300

log₂(2x-6) = 6

x = 35

400

log₄(5x - 1) = 3

x= 13

500

log_x(1/25) = -2

x= 5

Solving e

100

e^x-2=12

x = ln 56 +2 

200

4e^2x=8

x= ln (2) / 2

300

2e^x-3 = 1

x = ln 2

400

-3e^2x+16 = 5

x = (ln 3) / 2

500

4e^2x+2 = 16

x = (ln 3.50)/ 2

Extra

100

y = -3 ln (x+2) -1

Name the parent function

ln (x) 

200

y = 6 log (x-1)+2

Name parent function

log (x)

300

log (5x) = log 15

x = 3

400

log (x) = log (x²-56)

x = 8

500

ln (x²-28) = ln (-3x)

x =-7