Unit 6.1 & 6.2 Quiz Prep

Logs to Exponential

1

Rewrite in exponential form

 log_b⁡a=z 

 b^z=a 

2

Rewrite in exponential form

 log_b⁡9=m 

 b^m=9 

3

Rewrite in exponential form

 log_2⁡x=7 

 2^7=x 

4

Rewrite in exponential form

 log_2⁡64=6 

 2^6=64 

5

Rewrite in exponential form

 log_7⁡〖1/7〗=-1 

 7^(-1)=1/7 

6

Rewrite in exponential form

 log_(1/5)⁡〖1/25〗=2 

 〖1/5〗^2=1/25 

Exponential to Logs

1

Rewrite in logarithmic form

 r^z=k 

 log_r⁡k=z 

2

Rewrite in logarithmic form

 a^m=4 

 log_a⁡4=m 

3

Rewrite in logarithmic form

 3^5=y 

 log_3⁡y=5 

4

Rewrite in logarithmic form

 4^3=64 

 log_4⁡64=3 

5

Rewrite in logarithmic form

 5^6=15625 

 log_5⁡15625=6 

6

Rewrite in logarithmic form

 〖1/8〗^(-1)=8 

 log_(1/8)⁡8=-1 

Key Features / Transformations

1

What is the Domain of all exponential functions? 

All real numbers

2

The graph of an exponential function will always approach the ___________   ______________.

Horizontal Asymptote

3

For range, if the graph is above the horizontal asymptote is it y>  or y<

y>

4

What is the Horizontal Asymptote?

 5(9)^(x-5)+3 

 y = 3 

5

Describe the transformation.

 3(4)^(x-2)-8 

Right 2, Down 8

6

Describe the transformation.

 4(3)^(x+6)+7 

Left 6, Up 7

Expand the Log

1

Expand the logarithm

 log_8⁡(m∙w∙t) 

 log_8⁡m+log_8⁡w+log_8⁡t 

2

Expand the logarithm

 log_4⁡( h/m ) 

 log_4⁡h-log_4⁡m 

3

Expand the logarithm

 log_7(a∙m)^2  

 2log_7⁡a+2 log_7⁡m 

4

Expand the logarithm

 log_5⁡( j/k )^3  

 3log_5⁡j-3log_5⁡k 

5

Expand the logarithm

 log_2⁡(a^2∙t) 

 2 log_2⁡a+log_2⁡t 

6

Expand the logarithm

 log_3⁡(w^9/p^6 ) 

 9log_3⁡w-6 log_3⁡p 

Condense the Logs

1

Condense the expression to a single logarithm.

 log_4⁡a+log_4⁡b+log_4⁡c 

 log_4⁡(a∙b∙c) 

2

Condense the expression to a single logarithm.

 log_6⁡x-log_6⁡y 

 log_6⁡( x/y ) 

3

Condense the expression to a single logarithm.

 9log_6⁡a-9 log_6⁡w 

 log_6(⁡a^9/w^9 ) 

4

Condense the expression to a single logarithm.

 6 log_8⁡h+6log_8⁡a 

 log_8⁡(h^6∙a^6 ) 

5

Condense the expression to a single logarithm.

 4log_3⁡x+log_3⁡y 

 log_3⁡(x^4∙y) 

6

Condense the expression to a single logarithm.

 3log_5⁡b-8log_5⁡p 

 log_5⁡(b^3/p^8 )