SOLUTION: Find the exact solution, using common logarithms. log(x − 3) − log(5x − 7) = log(1/x)

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Question 1147951: Find the exact solution, using common logarithms.
log(x − 3) − log(5x − 7) = log(1/x)

Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!






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note: original equation was .

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


NO! The two solutions do NOT both work!

The given equation is

(1) log(x − 3) − log(5x − 7) = log(1/x)

To start solving that, you use rules of logarithms:

(2) log((x-3)/(5x-7)) = log(1/x)

Working from there, you find apparent solutions x=1 and x=7.

And those solutions both work in (2).

BUT... they have to satisfy the ORIGINAL equation. And x=1 does not, because it results in trying to take the logarithm of a negative number.

ANSWER: x=7 is the only solution.


Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

Had you answer as @josgarithmetic did,  you immediately would get the score from  "1"  to  "2"  of  4  from your teacher.



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