Apply logarithm property:

`log M^p=plogM ` or

`plogM=logM^p ` (1)

Substitute 3 for p and 7 for M in (1)

`3log7=log7^3= log343 `

Simplify the original expression:

`log5-3log7=log5-log343 `

Apply logarithm property:

`log(M/N)=logM-logN ` or

`logM-logN=log(M/N)` (2)

Substitute 5 for M and 343 for N in (2)

` log5-log343=log(5/343)`

**Therefore `log5-3log7=log(5/343) ` **