Evaluate using the properties of log

Question

given that loga^2=0.693 , loga^6=1.792 , loga^5=1.609

find loga^60

Answer 1

Rewrite the log using the properties.

 

loga⁶⁰= log(a³⁰ a³⁰)

 

         = 2loga³⁰

 

         = 2log((a⁶)⁵)

 

         = 10loga⁶

 

         = 3 * 10loga²

 

         = 30loga²

 

         = 30(0.693)

Answer 2

log 60 = log (2 · 5 · 6)

log 60 = log 2 + log 5 + log 6

 

Can you continue?