Expand and condense using the properties of logs?

Question

Expand:

 

log( 3xy^2/wz^4).

 

Condense:

 

2ln (x+2) + 1/2 ln y - 4ln z

 

 

Thanks in advance!

Answer 1

log (3xy²/wz⁴)

log 3xy² - log wz⁴

log 3 + log x + log y² - (log w + log z⁴ )

log 3 + log x + 2log y - log 2 - log z⁴

log 3 + log x + 2logy - log2 - 4log z

 

2ln (x + 2) + 1/2 ln y - 4lnz

ln (x + 2)² + ln y^1/2 - ln z⁴

ln { ((x + 2)² y^1/2 ) / z⁴ }