IM 3 - Logs Quiz Review

Find Inverse Functions

100

g(x)=4sqrt(x-1)

Find 

g^-1(x)

g^-1(x)=(1/4x)^2+1

g^-1(x)=1/16x^2+1

200

f(x)=9^(x-1)

Find 

f^-1(x)

f^-1(x)=log_9x+1

300

c(x)=log(x)

Find 

c^-1(x)

c^-1(x)=10^x

400

h(x)=log_4(x-1)

Find 

h^-1(x)

h^-1(x)=4^x+1

500

s(x)=1/2*10^(x-2)

Find 

s^-1(x)

s^-1(x)=log(2x)+2

Evaluate Logs

100

Evaluate

log_6 216

3

200

Evaluate

log100

2

300

Evaluate

ln1

0

400

Evaluate

log_16(1/64)

-3/2

500

Evaluate

log_3 root5(243)

1

Rewrite Logs and Exponentials

100

Rewrite in logarithm form:

7^x=35

log_7 35=x

200

Rewrite in exponential form (Do not solve for x):

log_2(x+1)=8

2^8=x+1

300

Rewrite in exponential form (Do not solve for x):

ln(5x)=x+1

e^(x+1)=5x

400

Rewrite in logarithm form (Do not solve for x):

e^(5x^2+1)=x+3

ln(x+3)=5x^2+1

500

Rewrite in exponential form (Do not solve for x):

log_(x+1)5=2x-3

(x+1)^(2x-3)=5

Simplify Logs and Exponentials

100

Simplify:

(2e^x)^3

8e^(3x)

200

Simplify:

6^(log_6 (3x)

3x

300

Simplify:

e^ln40

40

400

Simplify:

log_2 2^8

8

500

Simplify:

3log_2 4

6

Graph Logs and Exponentials

100

Describe the transformation (if any) and identify the domain, range, and asymptote:

y=e^x

No transformation

Domain: all real numbers

Range: y>0

H.A.: y=0

200

Describe the transformation (if any) and identify the domain, range, and asymptote:

f(x)=logx

No transformation

Domain: x>0

Range: all real numbers

V.A.: x=0

300

Describe the transformation (if any) and identify the domain, range, and asymptote:

y=log_5(x-3)-2

Tranformation: Right 3 units, Down 2 units

Domain: x>3

Range: all real numbers

V.A.: x=3

400

Describe the transformation (if any) and identify the domain, range, and asymptote:

y=e^(x+1)-3

Transformation: Left 1 unit, Down 3 units

Domain: all real numbers

Range: y>-3

H.A.: y=-3

500

Describe the transformation (if any) and identify the domain, range, and asymptote:

y=-3log_2(x+1)+3

Transformation: left 1 unit, up 3 units, vertical stretch by factor of 3, reflection over x-axis

Domain: x>-1

Range: all real numbers

V.A.: x=-1