SOLUTION: If log3(x − 3) − log 1/3(x + 1) is expressed in terms of a logarithm with base 9 .How is going to be ?

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Question 1180051: If log3(x − 3) − log 1/3(x + 1) is expressed in terms of a logarithm with base 9 .How is going to be ?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Expression does not clearly show what you have.
log%289%2C%283%28x-3%29%29%29-log%289%2C%281%2F3%28x%2B1%29%29%29 ?

log%289%283%28x-3%29%29%29-log%289%2C%28%281%2F3%29%28x%2B1%29%29%29 ?

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Your notation is indeed unclear....

For the problem to make sense, I believe the given expression is this:

log%283%2C%28x-3%29%29-log%281%2F3%2C%28x%2B1%29%29

To write this expression using base 9 logs, note

9+=+3%5E2
and
9+=+%281%2F3%29%5E%28-2%29

Then

log%283%2C%28x-3%29%29=2log%289%2C%28x-3%29%29
log%281%2F3%2C%28x%2B1%29%29=-2log%289%2C%28x%2B1%29%29

Then



The expression can then be written in various forms:

2log%289%2C%28%28x-3%29%28x%2B1%29%29%29

log%289%2C%28%28x-3%29%28x%2B1%29%29%5E2%29