Simplify Logs & Natural Logs

Simplify: log 10⁵

• 10

• 5

• 10

• can't be simplified

Simplify: $2\ln5$  

• can't be simplified

•  $\ln10$  

•  $\ln7$  

•  $\ln5^2$  

Simplify: $\ln e$  

•  $e$  

•  $\ln1$  

•  $1$  

• can't be simplified

 $\ln$ is 

• a common log

• a natural log

• Euler's number

• the most simplified form of a log

 $\log_37$ is equivalent to 

•  $\frac{\log7}{\log3}$  

•  $\frac{\log3}{\log7}$  

•  $\log\left(3\cdot7\right)$  

•  $\log\left(\frac{7}{3}\right)$  

 $\log_bb^x=b^{\log_bb^x}$  

• Product Property

• Inverse Property

• Quotient Property

• Change of Base Rule

 $\log\left(m\cdot n\right)=\log m+\log n$  

• Inverse Property

• Power Property

• Product Property

• Quotient Property

 $\log_bm=\frac{\log m}{\log b}$  

• Quotient Property

• Change of Base Rule

• Product Property

• Inverse Property

 $k\cdot\log_bm=\log_bm^k$  

• Power Property

• Quotient Property

• Inverse Property

• Product Property

 $\log\left(\frac{m}{n}\right)=\log m-\log n$  

• Product Property

• Inverse Property

• Change of Base Rule

• Quotient Property