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how do i solve 5 log(3) + log(4)?

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user4791387 | eNotes Newbie

Posted June 2, 2013 at 4:43 PM via web

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how do i solve 5 log(3) + log(4)?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted June 2, 2013 at 5:01 PM (Answer #1)

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You need to use the following logarithmic identities, such that:

`b*log a = log a^b`

`log a + log b = log (a*b)`

Reasoning by analogy yields:

`5*log 3 = log 3^5`

Replacing `log 3^5` for `5*log 3` and using the next logarithmic identity yields:

`log 3^5 + log 4 = log (4*3^5) = log 972`

Hence, evaluating the logarithmic expression, using logarithmic identities, yields `5*log 3 + log 4 = log 972.`

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