8.4 & 8.5 Quiz

Expand  $\log_8\left(xyz^6\right)$  

• 6log₈(xyz)

• log₈(x) - log₈(y) - 6log₈(z)

• log₈(x) + log₈(y) - log₈(z)

• log₈(x) + log₈(y) + 6log₈(z)

Condense
 $6\log x-3\log y$  

• log (xy³)

• log (x⁶ − y³)

• log (x⁶/y³)

• log (x⁶ + y³)

Expand the following logarithm: 
log₂ 6/y 

• log₂ 6 - log₂ y 
• log₂ y - log₂ 6 
• 2log 6 + 2log y
• log₂ 6 - y

Condense
 $2\log_4x-3\log_4y$  

•  $\log_4\left(x^2y^3\right)$  

•  $\log_4\left(\frac{x^2}{y^3}\right)$  

•  $\frac{2}{3}\log_4\left(\frac{x}{y}\right)$  

•  $\log_4\left(\frac{2x}{3y}\right)$  

Use properties of logs to expand.
 $\log_3\left(\frac{\sqrt{x}}{9}\right)$  

•  $\frac{1}{2}\log_3x\ +2$  

•  $2\log_3x\ +2$  

•  $2\log_3x-2$  

•  $\frac{1}{2}\log_3x\ -2$  

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

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

Expand the following logarithm: 
log_b x²y/z³  

• log_b 2x + log_b y - log_b 3z
• 2log_b x + log_b y - 3log_b z
• 2log_b x + log_b y + 3log_b z
• 2log_b x - log_b y - 3log_b z

Solve for x:  $\log_42x\ +\ \log_4\left(x-2\right)=2$  

• -2,4

• 2

• -2

• 4

Solve:
log₉(x)+log₉(x+2)=log₉(35)

• 5
• -7
• 5, -7
• -7, -13

The common logarithm has what base?

• 10
• 0
• e
• -e