Question

log( x2+2x+ 1) – log( x+1) = log 3

Answer 1

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To Solve:

• log(x² + 2x + 1) – log(x + 1) = log 3

Step-wise-Step Explanation:

By using the logarithm rule

➝ $\rm{ log_{b}(m) - log_{b}(n) = log_{b }( \frac{m}{n} ) }$

Where m = x² + 2x + 1 and n = x + 1.

Plugging the values according to the law,

➝ $\rm{ log( \dfrac{ {x}^{2} + 2x + 1 }{x + 1} ) = log(3) }$

Removing log from both sides and equating,

➝ $\rm{ \dfrac{ {x}^{2} + 2x + 1 }{x + 1} = 3}$

Cross multiplying,

➝ $\rm{ {x}^{2} + 2x + 1 = 3x + 3}$

Shifting the terms and solving,

➝ $\rm{{x}^{2} + 2x + 1 - 3x - 3 = 0}$

➝ $\rm{ {x}^{2} - x - 2 = 0}$

Solving for x using middle term factorisation,

➝ $\rm{ {x}^{2} - 2x + x - 2 = 0}$

➝ $\rm{x(x - 2) + 1(x - 2) = 0}$

➝ $\rm{(x - 2)(x + 1) = 0}$

Then, x = 2 or -1

Now:

Now if we substitute -1 in place of x, x + 1 will become 0 and log 0 is not defined. Hence, the only value of x is 2 (Answer)