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log (x+2) - log x = log 5

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seedrasoso | Student, Grade 10 | eNoter

Posted August 3, 2010 at 7:57 AM via web

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log (x+2) - log x = log 5

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted August 3, 2010 at 7:59 AM (Answer #1)

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log (x +2) - log x = log 5

We know that log a - log b = log (a/b)

==> log (x+2)/x = log 5

==> (x+2)/x = 5

Now cross multiply:

==> x + 2 = 5x

==> 2 = 4x

==> 2/4 = x

==> x= 1/2

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kjcdb8er | Teacher | (Level 1) Associate Educator

Posted August 3, 2010 at 8:00 AM (Answer #2)

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use the rule that log(A) - Log(B) = log (A/B)

so log (x+2) - log x = log 5

log((x+2)/x) = log 5

x + 2 / x = 5

x + 2 = 5x

2 = 4x

1/2 = x

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