Logarithmic

Algebra Level 3

Let y y be a Real Number such that y = λ ( log ⁡ ( − x ) + log ⁡ x ) y = \lambda (\log (-x) + \log x) .

If λ = ( log ⁡ ( − x ) + log ⁡ x ) 2 \lambda = (\log (-x) + \log x)^2 provided that x ∈ R x \in \mathbb{R} .

Find the maximum value of y y .

log 2 No solution log 5 log 6 log 3

Paul Ryan Longhas by Paul Ryan Longhas , 24, Philippines

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1 solution

Paul Ryan Longhas
Aug 30, 2015

If x ∈ R x \in \mathbb{R} then l o g ( − x ) + l o g x log(-x) + log x is either not defined or not real number. But, y = λ ( l o g ( − x ) + l o g x ) y=λ(log(-x)+logx) and y ∈ R y \in \mathbb{R} . Therefore, it is a contradiction. Thus, the answer is no solution.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

If we purely talk on reals, then sure. Otherwise there should be a solution...

Gian Sanjaya - 5 years, 9 months ago

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