Topic 5 - Exponential And Logarithmic Functions

Flip the Script

100

Convert to an logarithmic function:

2³ = 8 

What is log₂8 =3?

200

Convert to a exponential equation: 

log₅25=2

What is 5²=25?

300

Convert to a logarithmic equation: 

10^x=1000

what is log 1000 = x?

400

Convert to an exponential equation:

ln 7 = x 

What is e^x=7 ?

500

Convert to a logarithmic equation: 

e^3x = 15

What is ln15=3x?

Log It In

100

Evaluate: 

log₂8

What is x = 3 ? 

2^x=8

2^x=2³

x = 3 

200

Evaluate: 

log₉1

What is x =0? 

9^x=1

300

Evaluate:

log₅(1/125) 

what is x =-3 ?

5^x= (1/125)

5^x=5^-3

^x=-3 

400

Evaluate: 

lne⁴

What is x=4?

lne⁴=x

e^x=e⁴

^x=4

500

Evaluate: 

log₂₄₃3 

What is x = 1/5 ?

243^x=3

(3⁵)^x = 3¹

^{5x = 1} 

^{x = 1/5}

Graph It Like Its Hot

100

What is the parent function of the following: 

f(x)= log₄(x+2)-3

What is f(x)=log₄(x)?

200

Describe the transformation: 

g(x) = log₂(x+4) - 5

What is left 4 down 5?

300

Given: g(x) = log3(x+2) - 4

What is the domain? 

What is the range? 

What is the asymptote?

What is 

Domain: (-2,∞ )

Range: (-∞,∞ )

Asymptote: x = -2

400

Describe the transformation:

f(x) = -1/2log₂(x+1)-5

What is 

reflect across x axis 

Compress by 1/2

left 1 

down 5

500

Graph the following function: 

f(x) = log₅(x-1)+3 

_{HINT (MAKE A TABLE)} 

*check students work*

Log Laws in Action

100

Expand: 

log₃(5x)

What is log₃5+log₃x ?

200

Condense: 

2log₂a+3log₂b

What is log₂a²b³?

300

Expand:

ln(2x³/y²)

ln2+3lnx-2lny

400

Condense: 

log₇x-log₇4-log₇y

What is 

log₇(x / 4y) ?

500

Expand: 

log₄(3x³y²/z)

log₄3+3log₄x+2log₄y-log₄z

Solve for X-treme

100

Solve: 

log₄(2x+4)=3

What is x=30?

200

Solve: 

log(4k-5) = log(2k-1)

What is k =2?

4k-5=2k-1

2k=4

k=2

300

Solve for x:

4^x+1=8^x-2

What is x=8?

400

Solve: log₂(2x)+log₂(x-6)=5

What is x = 8 is a solution, x = -2 is extraneous? 

log₂(2x)+log₂(x-6)=5

2x²-12x-32=0

2(x²-6x-16)=0

2(x-8)(x+2)=0

500

Solve(round to the nearest thousandth): 

2^x+2 - 5= 20

What is x = 2.644 ?