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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