Question

Simplify
2 log 3x + log (x + 1) - log (x² - 1)
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Answer 1

$2 log 3x + log (x + 1) - log (x^2 - 1)$ is simplified as $log (\frac{9x^2}{(x-1)})$ .

Step-by-step explanation:

Here we have , 2 log 3x + log (x + 1) - log (x² - 1) or$2 log 3x + log (x + 1) - log (x^2 - 1)$

⇒  $2 log 3x + log (x + 1) - log (x^2 - 1)$          { $alogb = logb^a$ }

⇒  $(log (3x)^2) + log (x + 1) - log (x^2 - 1)$     { $loga -logb = log(\frac{a}{b})$ }

⇒  $(log (3x)^2) + log (\frac{(x + 1)}{(x^2 - 1)})$

⇒  $log 9x^2 + log (\frac{(x + 1)}{(x^2 - 1)})$

⇒  $log 9x^2 + log (\frac{(x + 1)}{(x-1)(x+1)})$

⇒  $log 9x^2 + log (\frac{1}{(x-1)})$

⇒  $log 9x^2 + (-1)log(x-1)$               { $log(\frac{1}{b}) = -logb$ }

⇒  $log 9x^2 -log(x-1)$

⇒  $log (\frac{9x^2}{(x-1)})$

$2 log 3x + log (x + 1) - log (x^2 - 1)$ is simplified as $log (\frac{9x^2}{(x-1)})$ .