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Solve for x given that log(2)x + log (4)x +log(8)x = 11 ( the number in brackets is the...

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xetaalpha2 | Student | Honors

Posted March 23, 2011 at 2:52 PM via web

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Solve for x given that log(2)x + log (4)x +log(8)x = 11 ( the number in brackets is the base.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 23, 2011 at 3:01 PM (Answer #1)

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We have to solve log(2)x + log (4)x +log(8)x = 11.

Use the relation log(a) b = log b/ log a, for any common base.

log(2)x + log (4)x +log(8)x = 11

can be written as log to the base 2

=> log(2)x + log(2)x/log(2)4 + log(2)x/log(2)8 = 11

=> log(2)x + log(2)x/2 + log(2)x/3 = 11

=> log(2)x [ 1 + 1/2 + 1/3] = 11

=> log(2)x [ 11/6] = 11

=> log(2) x = 6

=> x = 2^6

=> x = 64

The required value is x = 64

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