Logarithmic properties

Write log_b(xy) as two logs

• log_bx+log_by

• log_bx-log_by

• log_bx*log_by

• log_bx/log_by

Write log_b(x/y) as two logs

• log_bx-log_by

• log_bx+log_by

• log_bx*log_by

• log_bx/log_by

Evaluate log_b(b)

• -1

• 0

• 1

• b

Simplify log₄4^3x

• 3x

• 3

• 4

• 4^3x

Write the expression as a single logarithm.   Then simplify if possible.
log₅3 + log₅6 + log₅9

• log₅69

• log₅56

• log₅162

• log₅98

The common logarithm has what base?

• 10

• 0

• e

• -e

 $\log_210+\log_25=$  

•  $\log_250$  

•  $\log_215$  

•  $\log_415$  

•  $\log_450$  

 $\log_{10}\left(\frac{3}{7}\right)=$  

•  $\frac{\log\ 3}{\log_{ }7}$  

•  $\log\ 3-\log\ 7$  

•  $\log_73$  

•  $\frac{\log\ 30}{\log\ 70}$  

Condense  $5\ \log_2\ 12$  

•  $\log_2\ \frac{12}{5}$  

•  $\log_5\ \sqrt{12}$  

•  $\log_2\ 12^5$  

•  $\log_2\left(12\times5\right)$  

Condense:  $2\log_5\left(x\right)+3\log_5\left(y\right)$  

•  $\log_5\left(x^2\right)+\log_5\left(y^3\right)$  

•  $\log_5\left(2x\right)+\log_5\left(3y\right)$  

•  $2\log_5\left(x\right)\cdot3\log_5\left(y\right)$  

•  $\log_5\left(x^2y^3\right)$