Review for Logarithms Quiz

Review for Logarithms Quiz

Switching from Logarithmic Form to Exponential form  $\log_bx=y\ \ \leftrightarrow\ \ b^y=x$  

 $\log_39=2\ \ \leftrightarrow\ \ 3^2=9$  

Multiple Select

Write the logarithm in exponential form:  $\log_381=4$  

•  $3^4=81$  

•  $4^3=81$  

Multiple Select

Write the logarithm in exponential form:  $\log_28=3$  

•  $2^8=3$  

•  $2^3=8$  

What does a logarithm mean?  $\log_bx=y$  

"How many times do we multiply b  to get x ? We multiply b "y-times" to get x."

Multiple Choice

Evaluate:  $\log_864=$  

• 8

• 4

• 2

• 3

Multiple Choice

Evaluate:  $\log_5125=$  

• 5

• 3

• 25

• 4

A logarithmic function is the inverse of an exponential function.

Proof:

  $\log_bx=y$  

Switch x and y
 $\log_by=x$  
Solve for y by rewriting in exponential form 
 $b^x=y$  
Therefore, the inverse of  $\log_bx=y$  is  $b^x=y$  

Multiple Choice

Write the inverse function of:  $\log_5x=y$  

•  $5^x=y$  

•  $x^5=y$  

Multiple Choice

Write the inverse function of:  $\log_9x=y$  

•  $x^9=y$  

•  $9^x=y$  

Change of base formula

 $\log_bm=\frac{\log m}{\log b}$  

(base b goes in the basement)

Multiple Choice

Write logarithm in exact form by using the change of base formula:
 $\log_47$  

•  $\frac{\log7}{\log4}$  

•  $\frac{\log4}{\log7}$  

Multiple Choice

Write logarithm in exact form by using the change of base formula:
 $\log_{34}17$  

•  $\frac{\log34}{\log17}$  

•  $\frac{\log17}{\log34}$  

Graphing $y=\log_bx$ 

The graph of $y=\log_bx$ is obtained by reflecting $y=b^x$ across the $y=x$  line.


Domain:  $x>0$  (you cannot take the log of 0 or negative numbers)
Range: All real numbers /  $\left(-\infty,\infty\right)$