Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

Trending News

Promoted
?
? asked in Science & MathematicsMathematics · 8 years ago

Solve the following logarithmic equation.?

log (x-5) + log (x+2) = log (x+3)

Round off answer to 4 decimal places. Or choose "no solution."

2 Answers

Relevance
  • Ben
    8 years ago
    Favorite Answer

    Combine logs:

    log ((x-5)(x+2)) = log (x+3)

    So (x-5)(x+2) = (x+3)

    x² - 3x - 10 = x + 3

    x² - 4x - 13 = 0

    (x-2)² = 13 + 4

    x - 2 = ±√17

    x = 2 ± √17

    Cannot take log of negative numbers, so x - 5 > 0 is a requirement.

    This means x = 2 + √17 = 6.1231

  • Rogue
    Lv 7
    8 years ago

    log (x-5) + log (x+2) = log (x+3)

    give log(a) + log(b) = log(ab)

    => log((x-5)(x+2)) = log (x+3)

    => (x-5)(x+2) = x +3

    => x^2 -3x -10 = x + 3

    => x^2 -4x = 13

    => x^2 -4x + 4 = 17

    => (x - 2)^2 = 17

    => x -2 = ±√17

    => x = 2±√17

    as 2-√17 will result in a log of a negative number in the original question it not a valid solution.

    => x = 2+√17

    => x = 6.1231 (4 dp)

Still have questions? Get your answers by asking now.