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Mathematics 18 Online
OpenStudy (anonymous):

Is anybody really good at logs and is willing to help me study for my finals? Please:/

OpenStudy (anonymous):

Unfortunately I only have basic knowledge of logarithims, sorry. Good luck finding someone!

OpenStudy (anonymous):

Well basic is pretty much what I need help on, I don't want to burden you with helping if you're busy

OpenStudy (solomonzelman):

Just a couple of basic rules, \(\large\color{black}{ 1)~~~ \log_w(a)+\log_w(b)=\log_w(a\times b) }\) (addition of logs)) \(\large\color{black}{ 2)~~~ \log_w(a)-\log_w(b)=\log_w(a\div b) }\) (difference of logs) \(\Large\color{black}{ 3)~ \log_cd=\frac{\log(c)}{\log(d)} }\) (change in base) \(\large\color{black}{ 4)~~~ \log(a)= \log_{10}(a) }\) (unspecified base)

OpenStudy (solomonzelman):

are you familiar with these rules?

OpenStudy (anonymous):

#'s 3 & 4 are the rules I recognize

OpenStudy (solomonzelman):

So, you don't know 1 and 2, right? and Also, \(\large\color{black}{ 5)~~~ \log_AB=C~~~~\rightarrow~~~~~~A^C=B }\) \(\large\color{black}{ 6)~~~ \log_w(a^k) =k\log_w(a) }\)

OpenStudy (anonymous):

Yes, I've seen those before as well. Is it possible for you to help me on individual questions?

OpenStudy (solomonzelman):

yes.. sure:)

OpenStudy (solomonzelman):

post it here....

OpenStudy (anonymous):

\[\left( \frac{ 8 }{ 5 } \right)^{x}=\frac{ 25 }{ 64 }\]

OpenStudy (solomonzelman):

Take log of both sides, \(\large\color{black}{\log (\frac{8}{5})^x =\log(\frac{25}{64}) }\)

OpenStudy (anonymous):

Okay, so I would just have to add the log or do I still need to move things around?

OpenStudy (solomonzelman):

log(8/5) =? (rule 2)

OpenStudy (anonymous):

I would have to use difference of logs?

OpenStudy (solomonzelman):

yes.

OpenStudy (solomonzelman):

but, before we do this, can you bring the exponent on the outside of log? (referring to rule 6)

OpenStudy (anonymous):

That's quite confusing, I don't understand what numbers to plug into a and b

OpenStudy (solomonzelman):

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