Writing expression as a sum and /or diference of logarithms

[charlesjoy]

Good morning. worked the following problem but have a hard time understanding the reasoning/logic behind it. Am I working it corectly?

log 6r^2s^5

My answer: log 12r + log 5s

 

[Loren]

It's hard to tell what is meant because you have not included grouping symbols.

I believe the order of operations implies that log 6r^2s^5 means \(\displaystyle (\log 6r^2)s^5\).

Maybe you could clarify by using parenthesis.

 

[charlesjoy]

Your example is what is in the book but there is not parenthesis.

 

[Deleted member 4993]

Good morning. worked the following problem but have a hard time understanding the reasoning/logic behind it. Am I working it corectly? <<<No.

log 6r^2s^5

You should be able to do this now - from previous examples that we helped you solve.

\(\displaystyle log (6r^2s^5) = log (6) \, + \, log(r^2) \, + \, log(s^5)\)

Now continue....


My answer: log 12r + log 5s

 

[Loren]

I assume that log 6r^2s^5 means \(\displaystyle (\log 6r^2)s^5\).

\(\displaystyle \log 6r^2 = \log 6+\log r^2 = \log 6 + 2\log r\) and that is multiplied by s[sup:3kha1u5v]5[/sup:3kha1u5v] giving you \(\displaystyle s^5(\log 6 + 2\log r)\) or \(\displaystyle s^5\log 6 + 2s^5\log r\).

Please understand, that is a strict application of the order of operations which says to apply the exponents first from left to right, then the multiplication from left to right. Furthermore, an exponent only operates on the symbol immediately to its left.