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Solve for x: log(base 6)(x - 2) + log(base 6)(x + 3) = 2 If there are multiple...

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted August 20, 2013 at 4:33 AM via web

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Solve for x:

log(base 6)(x - 2) + log(base 6)(x + 3) = 2

If there are multiple answers, separate them with a comma.

1 Answer | Add Yours

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted August 20, 2013 at 4:44 AM (Answer #1)

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`log_6(x-2)+log_6(x+3) = 2`

Using rules of logarithm;

`loga+logb = log(ab)`

If `y = log_a(b)` then `b = a^y`

`log_6((x-2)(x+3)) = 2`

`(x-2)(x+3) = 6^2`

`x^2+3x-2x-6 = 36`

`x^2+x-42 = 0`

`x^2+7x-6x-42 = 0`

`x(x+7)-6(x+7) = 0`

`(x+7)(x-6) = 0`


x = -7 and x = 6.

Since we have logarithm negative answers are not suited always to satisfy the equation.

So the best answer is x = 6.

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