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

Expert Answers
flbyrne eNotes educator| Certified Educator

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) `

adarshanurag | Student

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)

tonys538 | Student

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)