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Solve the equation log (x^2 + 18x + 16) = 10

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lxsptter | Student, Undergraduate | Valedictorian

Posted May 6, 2013 at 2:42 AM via web

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Solve the equation log (x^2 + 18x + 16) = 10

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 6, 2013 at 2:51 AM (Answer #1)

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The equation `log(x^2 + 18x + 16) = 10` has to be solved.

log refers to logarithm to the base 10. If `log_b x = n => x = b^n`

`log(x^2 + 18x + 16) = 10`

=> `x^2 + 18x + 16 = 10^10`

=> `x^2 + 18x + 16 - 10^10 = 0`

`x = (-18 +- sqrt(18^2 - 4*(16 - 10^10)))/2`

= `-9 +- sqrt(81 - 16 + 10000000000)`

= `-9 +- sqrt(10000000065)`

The solution of the given equation is `-9 +- sqrt(10000000065)`

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