Properties of Logs

The common logarithm has what base?

• no base

• 1

• 0

• 10

Condense

• d

• b

• a

• c

 $\log_212+3\log_2x^2$   

Write as a single log:  

•  $\log_215x^2$  
  

•  $\log_236x^6$  

•  $\log_212x^6$  

•  $\log_2x15^2$  

 $\log_425=x$  

Evaluate to 3 decimal places:

Write the expression as a single logarithm. Then simplify if possible.
  $\log_53+\log_56+\log_59$  

•  $\log_556$  

•  $\log_5162$  

•  $\log_598$  

•  $\log_5168$  

Condense

• a

• d

• c

• b

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81

• log₃81 = 4

• log₈₁3 = 4

• log₄81 = 3

 $\log_2288-\frac{1}{2}\cdot\log_281$  

Condense into a single logarithm:

•  $\log_232$  

•  $\log_2\left(\frac{32}{9}\right)$  

•  $\log_255$  

•  $\log_2207$  

 $\log_5\sqrt{ab^7}$  

Expand:

•  $\frac{1}{2}\log_5a+3.5\log_5b$  

•  $\frac{1}{2}\log_5a+b$  

•  $\frac{1}{3}\log_5b+\log_5a$  

•  $\frac{1}{2}\log_5ab^7$  

Expand:

• 1/3 log x + log y + log z

• 1/3 log x - 1/3 log y - 1/3 log z

• 1/3 log x + 1/3 log y + 1/3 log z

• 3 log x + 3 log y + 3 log z