Question

Rewrite the logarithm as a ratio of common logarithms and natural logarithms. log4 45

Answer 1

Common logarithm

`log_451= (log_1_045)/(log_1_08)`

Natural logarithms

`log_445= (log_e45)/(log_e4)`

or

`log_445= (In45)/(In4)`

Explanation:

From the question we are told that

`Log_445`

Generally converting log from base x to base 10 si mathematically represented as

`log_xa=log_1_0a *log_x10`

`log_xa= (log_1_0a)/(log_1_0x)`

Therefore

Common logarithm

`log_451= (log_1_045)/(log_1_08)`

Generally Natural logarithms
`log_ex\ or\ inx` is mathematically represented as

`log_xa= (log_ea)/(log_ex)`

Therefore

Natural logarithms

`log_445= (log_e45)/(log_e4)`

or

`log_445= (In45)/(In4)`