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Solve the following logarithmic equation: `log_9 (x-5) + log_9 (x+3)=1`

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maheen100 | Student, Undergraduate | Honors

Posted June 10, 2012 at 12:20 AM via web

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Solve the following logarithmic equation: `log_9 (x-5) + log_9 (x+3)=1`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 10, 2012 at 2:34 AM (Answer #1)

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The equation `log_9 (x-5) + log_9 (x+3)=1` has to be solved. Use the property of logarithms log a + lob = log(a*b)

`log_9 (x-5) + log_9 (x+3)=1`

=> `log_9(x - 5)(x + 3) = 1`

=> (x - 5)(x + 3) = 9

=> x^2 - 2x - 15 = 9

=> x^2 - 2x - 24 = 0

=> x^2 - 6x + 4x - 24 = 0

=> x(x - 6) + 4(x - 6) = 0

=> (x + 4)(x - 6) = 0

=> x = -4 and x = 6

But as the logarithm of negative numbers is not defined ignore x = -4.

The solution of the equation is x = 6

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