Logarithmic Properties & Change of Base

Logarithmic functions are the inverse of...

• Linear Functions
• Exponential Functions 
• Quadratic Functions 
• Polynomial Functions 

The common logarithm has what base?

• 10
• 0
• e
• -e

Evaluate log_b(b)

• -1
• 0
• 1
• b

Condense

 $\log5-\log4$  

•  $\log\left(5-4\right)$  

•  $\log\left(\frac{4}{5}\right)$  

•  $\log\left(\frac{5}{4}\right)$  

•  $\log\left(5^{-4}\right)$  

Write the expression as a single logarithm.

 $\log_39+\log_324$  

•  $\log_3\left(\frac{9}{24}\right)$  

•  $\log_39+24$  

•  $\log_324^9$  

•  $\log_39\cdot24$  

Simplify:  $\log_73+\log_76$  

•  $\log_79$  

•  $\log_7\left(\frac{1}{2}\right)$  

•  $\log_718$  

•  $\log_7729$  

What is the expression as a single logarithm?

 $\log_27-\log_29$  

•  $\log_27-9$  

•  $\log_2\left(\frac{7}{9}\right)$  

•  $\log_27\cdot9$  

•  $\log_2\left(\frac{9}{7}\right)$  

Write as a single log: log 12 + 2 log x

• log (12 + 2x)
• log (14x)
• log (12 * 2x)
• log (12x²)

Write the expression as a single logarithm.   Then simplify if possible.
log 6 - log 3 + 2 log 7

• log 98
• log 78
• log 56
• log 45

Condense the following logarithm: 3 log₂ x + 2 log₂ y – 4 log₂ z 

• log₂ x³y²∕z⁴
• log₂ x³y²z⁴
• log₂ xyz⁹
• 9log₂ xyz