logarithmic properties review; expand and condense

log₅ 69

log₅ 56

log₅ 162

log₅ 98

 $\log_2\ \frac{12}{5}$  

 $\log_5\ \sqrt{12}$  

 $\log_2\ 12^5$  

 $\log_2\left(12\times5\right)$  

 $\log_3\left(x\right)\cdot\log_3\left(y\right)$  

 $\log_3\left(xy\right)$  

 $\log_3\left(\frac{x}{y}\right)$  

 $\frac{\log_{3\ }x}{\log_3\ y}$  

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

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

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

 $\log_5\left(x^2y^3\right)$  

 $\log_6\left(7\right)+\log_6\left(x^5\right)+\log_6\left(y\right)$  

 $\log_6\left(7\right)+5\log_6\left(x\right)+\log_6\left(y\right)$  

 $\log_6\left(7x^5\right)+\log_6\left(y\right)$  

 $5\log_6\left(7x\right)+\log_6\left(y\right)$  

4 ln 3y - 3 lnx

ln3 + 4 lny - 3 lnx

4 ln x 3 lny - 3 lnx

ln3 + lny⁴ - lnx³

log a x log b

log a + log b

log a - log b

a log b

log a - log b

 $\frac{\log a}{\log b}$  

log_a b

log_b a

2log(a) + log(b)

2log(a) + 2log(b)

log(a) + log(b)

2log(a) * log(b)

$\log\left(xy^3\right)$

$\log\left(x^6-y^3\right)$

$\log\left(\frac{x^6}{y^3}\right)$

$\log\left(x^6y^3\right)$