Final Exam Review<3

Graphing Exponential

100

Graph the exponential f(x)=2^x

Domain: (-infinity,infinity)

Range: Y>0

End Behavior: x>infinity,f(x)>infinity 

Y=Intercept: (0,1)

X-Intercept: y=0

200

Graph the exponential f(x)=3^x

Domain: (-Infinity,infinity) 

Range: Y>0 

End Behavior: x>infinity, f(x)>infinity

x>-infinity,f(x)>0

Y intercept=(0,1)

Asymptote=Y=0

300

Graph the exponential f(x)=(1/2)^x

Domain: (-infinity, infinity)

Range: Y>0 

End Behavior: 

x--- infinity, f(x)--- 0

x--- -infinity,f(x)--- infinity

Y intercept=(0,1)

Asymptote=Y=0

400

Graph the exponential f(x)=(2/3)^x

Domain: IR

Range: Y>0 

End Behavior: 

x--- infinity, f(x)--- 0

x--- -infinity,f(x)--- infinity

Y intercept=(0,1)

Asymptote=Y=0

500

Graph the exponential f(x)=(5/2)^x

Domain: (-infinity, infinity)

Range: Y>0 

End Behavior: 

x--- infinity, f(x)--- 0

x--- -infinity,f(x)--- infinity

Y intercept=(0,1)

Asymptote=Y=0

Solving Exponential Equations

100

2^x+1=2⁹

x=8

200

5⁴ⁿ⁺⁵=5^n-7

n=-4

300

6^2x-10=36

x=6

400

125^y=25

y=2/3

500

27^2x=243^x-2

x=-10

Converting log to Exponential or Exponential to log

100

14²=196

log₁₄196=2

200

2^-3=1/8

log₂1/8=-3

300

log₉27=3/2

9^3/2=216

400

36^1/2=6

log₃₆6=1/2

500

log₄1/16=-2

4^-2=1/16

Condensing log/Exponential

100

4 x log₄ a + 2 x log₄ b

(log₄ a⁴ b²⁾

200

2 x log 6 - log 9

log 4

300

3 x log₂ 4-log₂ 32

log₂ 2

400

log₂ 15 + log₂ 4 - log₂ 6

log₂ 10

500

1/3(log₅ 8 + log₅ 27) - log₅ 3

log₅ 2

Expanding logs/Exponential

100

log (squarroot (7x³))

1/2(log 7 + 3 logx)

200

log₂(y/z⁵)²

2(log₂ y-5 log₂Z)

300

log₄(a⁹/b)

(9log₄ 9- log₄b)

400

log₃ ⁴(squareroot (m⁵n²))

1/4(5log₃m+2log₃n)

500

log₆(xyz⁴)

(log₆x+log₆y+4log₆z)