# how do i write log, 5 -3 log, 7 as a single logarithm ?

*print*Print*list*Cite

### 3 Answers

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) ` **

log 5 - 3 log 7

= log 5 - log 7^3 [ as, x log a = log a^x ]

= log 5 - log 343 [ as, log a - log b = log(a/b) ]

= log (5/343)

The expressionlog 5 -3 log 7 has to be written as a single logarithm.

Use the property of logarithm:

log a - log b = log(a/b)

a*log b = log b^a

log 5 -3 log 7

= log 5 - log 7^3

= log (5/7^3)

= log (5/343)