SOLUTION: write 5log(3x-11)-7log(x)as a single logarithm

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Question 201623This question is from textbook
: write 5log(3x-11)-7log(x)as a single logarithm This question is from textbook

Found 3 solutions by stanbon, jsmallt9, RAY100:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
write 5log(3x-11)-7log(x)as a single logarithm
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= log(3x-11)^5 - log(x)^7
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= log[(3x-11)^5/(x)^7]
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Cheers,
Stan H.

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
We need to understand the properties of logarithms (which are directly related to the properties of exposnents since logarithms are exponents):
  • a%2Alog%28%28b%29%29+=+log%28%28b%5Ea%29%29
  • log%28%28a%29%29+%2B+log%28%28b%29%29+=+log%28%28a%2Ab%29%29
  • log%28%28a%29%29+-+log%28%28b%29%29+=+log%28%28a%2Fb%29%29

The last two allow you to combine two log's into one, which is what you want. But they require that there is nothing (but a 1) in front of the log's. The first property allows you to remove unwanted coefficients.

Now we'll solve your problem to combine 5log%28%283x+-+11%29%29+-+7log%28%28x%29%29 into a single log. We will start by using the first property to remove the coefficients:
log%28%28%283x+-+11%29%5E5%29%29+-+log%28%28x%5E7%29%29
Now we will combine them using the third property (since it is subtraction):
log%28%28%28%283x+-+11%29%5E5%29%2F%28x%5E7%29%29%29%29

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
Remember alogb= logb^a,,,,and log a - log b = log (a/b)
.
5 log (3x-11) - 7 log(x )
.
log (3x-11)^5 - log (x)^7
.
log { (3x-11)^5 / (x)^7 }
.
check,,,,let x=5, both original and answer = -1.882