Unit 6 Prep (Honors)

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)^7  

 7 log_8⁡m+7 log_8⁡w+7 log_8⁡t 

2

Expand the logarithm

 log_4⁡( h/m )^6  

 6log_4⁡h-6 log_4⁡m 

3

Expand the logarithm

 log_7⁡(a^3∙m)^2  

  6log_7⁡a+2 log_7⁡m  

4

Expand the logarithm

 log_5⁡( j/k^4 )^3  

 3 log_5⁡j-12 log_5⁡k 

5

Expand the logarithm

 log_2⁡(a^2∙∛b) 

 2log_2⁡a+1/3 log_2⁡b 

6

Expand the logarithm

 log_3⁡( w^9/p^6 )^2  

 18log_3⁡w-12log_3⁡p 

Condense the Logs

1

Condense the expression to a single logarithm 

4 log_7⁡p+4 log_7⁡q+4 log_7⁡r 

log_7⁡(p∙q∙r)^4 or log_7⁡(p^4∙q^4∙r^4)

2

Condense the expression to a single logarithm

 5 log_3⁡h-4log_3⁡a 

 log_3⁡(h^5/a^4 ) 

3

Condense the expression to a single logarithm

 3log_4⁡a+2 log_4⁡m 

 log_4⁡(a^3∙m^2) 

4

Condense the expression to a single logarithm

 6 log_8⁡k-13 log_8⁡y 

 log_8⁡(k^6/y^13 ) 

5

Condense the expression to a single logarithm

 24 log_3⁡a-1/3 log_3⁡z 

log_3⁡(a^24/z^(1/3) ) or log_3⁡(a^24/∛z)

6

Condense the expression to a single logarithm 

 4 log_9⁡h+(log_9⁡p)/5