7.4B Properties of Logarithms & Change of Base

Write each expression as a single logarithm. All answers must be completely simplified.
1.  $\log_54+\log_53$  

•  $\log_57$  

•  $\log_51$  

•  $\log_512$  

• 0

Write each expression as a single logarithm. All answers must be completely simplified.

2.  $\log_625-\log_65$  

•  $\log_65$  

•  $\log_620$  
  

•  $\log_62$  
  

Write each expression as a single logarithm. All answers must be completely simplified.

3.  $\log_24+\log_22-\log_28$  

•  $0$  

• 1

• 2

• 8

Write each expression as a single logarithm. All answers must be completely simplified.

4.  $5\log_7x+2\log_7x$  

•  $\log_7x^7$  

•  $\log_7x^{10}$  

Write each expression as a single logarithm. All answers must be completely simplified.

5.  $\log_460-\log_44+\log_4x$  

•  $\log_4\frac{15}{x}$  

•  $\log_415x$  

•  $\log_456x$  

Write each expression as a single logarithm. All answers must be completely simplified.

6.  $\log7-\log3+\log6$  

•  $\log10$  

•  $\log\frac{7}{18}$  

•  $\log14$  

Write each expression as a single logarithm. All answers must be completely simplified.

7.  $2\log r-3\log s-4\log t$  

•  $\log\frac{1}{r^2s^3t^4}$  
  

•  $\log\frac{r^2}{s^3t^4}$  
  

Write each expression as a single logarithm. All answers must be completely simplified.

8.  $\frac{1}{3}\left(\log_2x-\log_2y\right)$  

• 
• 
• 

Write each expression as a single logarithm. All answers must be completely simplified.

9.  $\frac{1}{2}\log x+\log y-2\log z$  

•  $\log\sqrt{xyz^2}$  

•  $\log\frac{y\sqrt{x}}{z^2}$  

•  $\log\frac{\sqrt{xy}}{z}$  

Write each expression as a single logarithm. All answers must be completely simplified.

10.  $\log_5y-4\left(\log_5r+2\log_5t\right)$  

•  $\log_5\frac{y}{r^4t^8}$  
  

•  $\log_5\frac{yt^2}{r^4}$