Math 3A Ch.5 Logarithm Jeopardy

Converting

200

Convert to Logarithm Form

15^x=730

log_15(730)=x

400

Convert to Logarithm Form

x⁴=625

log_x(625)=4

600

Convert to Exponential Form

log_b(m)=w

b^w=m

800

Convert to Exponential Form

Log_(2b)(XY)=37

(2b)^37=XY

1000

Convert to Logarithm Form

3^(2x+1)=F

Log_3(F)=2x+1

Domain & Range

200

What is the Range for ALL Logarithm functions?

(-oo, oo)

ARN

400

What is the Domain of:

f(x)=log_2(x)

x>0

(0, oo)

600

What is the Domain of:

f(x)=2log(x+3)-5

(-3, oo)

x>-3

800

What is Domain of:

f(x)=log_2(x-1)-4

x>1

1000

What is Domain of:

f(x)=log_3(x+5)-4

x>-5

Transformation log Functions with Base 10

200

Shifted 3 units up and 5 units shifted to the left.

y=log(x+5)+3  or

y=log₁₀(x+5)+3

400

Shifted 2 units to the right & 5 units down

y=log(x-2)-5  or 

y=log₁₀(x-2)-5

600

Shifted 7 units up & 1 unit the left with a vertical stretch of 3.

y=3log(x+1)+7  or

y=3log₁₀(x+1)+7

800

Shifted 3 units to the right, shifted 11 units up, & reflected across the x-axis.  

y= -log(x-3)+11  or

y= -log₁₀(x-3)+11

1000

Reflected across the x-axis, shifted down 3 units, shifted to the left 6 units, and vertically compressed 1/2.

y= -1/2 log(x+6)-3  or

y= -1/2 log₁₀(x+6)-3

Solving Logarithms

200

log_x9=2

x=3

400

Solve for x:

log₂(x)=3

8

600

Solve for x:

log₂(x)=-1

1/2 or .5

800

log₁₆(64)=x

x=3/2

1000

log₆(4x-8)=2

x=11

Log Facts & Properties

200

What is the inverse equation of log_b(x)=y?

b^x=y 

400

That is the inverse function of  log₈(x-1)=y

y=8^x+1

600

For  log_b(x)=y , Why must the inputs be x>0 ?

Because of the asymptote, x=0, restricts our domain options.

800

log_bx=y

What happens to a log graph when 0<b<1 ?

The function is reflected across the x-axis

1000

log_bx=y

What values of b, DO NOT make sense? AKA for what values of b is y=log_bx not defined?

b<=0 and b=1

(in rare occasions, the graph would be discrete)

True or False

200

True or False: The value of log_b is positive

False: range is all real numbers

400

True or False: log_bx is not a valid expression if x is a negative number.

True because of our domain restrictions, x>0.

600

True or False:  log_b1=0 for any base, b>0.

True: b⁰=1 for b>0

800

True or False:  log_b(b)=1 for any b>0.

True because b¹=b

1000

True or False:  log₄(x) < log₆(x) for any value of x.

False  log₄(x) = log₆(x) when x=1

Evaluate

200

Evaluate the following expression

log₈(8)=

1

400

Evaluate the following expression

log₅(5^-4)=

-4

600

Evaluate the following expression

log₄(1)=

0

800

Evaluate the following expression

log₃(1/9)=

-2

1000

Evaluate the following expression

log₈(16)=

4/3