SOLUTION: Please help with this problem: 3 log 3 x=5 (the second "3" is under the word "log"). I can't seem to follow the pattern on my textbook. I would love to see the steps to workin

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help with this problem: 3 log 3 x=5 (the second "3" is under the word "log"). I can't seem to follow the pattern on my textbook. I would love to see the steps to workin      Log On


   

Question 12591: Please help with this problem: 3 log 3 x=5 (the second "3" is under the word "log"). I can't seem to follow the pattern on my textbook. I would love to see the steps to working out this problem. thanks!
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
3+%2Alog%283%2Cx%29+=+5+

There are probably several ways to go about this. I'd say to divide both sides by 3, and get
log%283%2Cx%29+=+5%2F3

Next use the basic definition of logarithms to convert to exponential form. Remember the definition says +log%28b%2Cx%29+=+y means b%5Ey+=+x?

In the same way, log%283%2Cx%29+=+5%2F3 means that 3%5E%285%2F3%29+=+x

What you are trying to find is x, and that's it!! x = 3%5E%285%2F3%29+.

Is that enough, or you could probably rewrite this as 3%2A+%283%5E%282%2F3%29+%29+ which means 3%2A+%28+root%283%2C9%29+%29, but that's getting carried away if you ask me. Easier to calculate it and say approximately 6.24.

R^2 at SCC