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

Expert Answers

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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) `

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