5.5 Logarithm Laws

log 10

log 21

log 3/7

log 3/log 7

$$\log_26$$  

$$\log_250$$  

$$\frac{\log_260}{\log_210}$$  

$$\log_270$$  

log 10

log 6

log 24

log 144

$$\log_65\ +\ \log_64\ +\ \log_6y$$  

$$\log_65\ -\ \log_64\ +\ \log_6y$$  

$$\log_65\ -\ \log_64\ -\ \log_6y$$  

$$\log_65\ -\ \log_64y$$  

$$\log\left(\frac{3x}{5x\ +\ 2}\right)$$  

$$\log\left(\frac{5x\ +\ 2}{3x}\right)$$  

$$\log\left(3x\left(5x+2\right)\right)$$  

$$\log\left(\frac{5x\ +\ 2}{3\ -\ x}\right)$$  

$$\log\left(\sqrt{x}y^5\right)$$  

$$\log_3\left(\sqrt{x}y^5\right)$$  

$$\log_3\left(5\sqrt{x}y\right)$$  

$$\log_3\left(xy\right)^{\frac{5}{2}}$$  

50

25

20

2

$$\log_8\left(\frac{a^2}{b^3c}\right)$$  

$$\log_8\frac{a^2}{3bc}$$   

  $$\log_8\left(2a3bc\right)$$  

$$\log_8\left(a^2-c+b^3\right)$$