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Problem If log a x = α \log_a x = \alpha log a x = α log b x = β \log_b x = \beta log b x = β log c x = γ \log_c x = \gamma log c x = γ log d x = δ \log_d x = \delta log d x = δ x ≠ 1 x \neq 1 x = 1 a , b , c , d ≠ 0 , > 1 a, b, c, d \neq 0, > 1 a , b , c , d = 0 , > 1 log a b c d x \log_{abcd} x log ab c d x ≤ α + β + γ + δ 16 \le \frac{\alpha + \beta + \gamma + \delta}{16} ≤ 16 α + β + γ + δ ≥ α + β + γ + δ 16 \ge \frac{\alpha + \beta + \gamma + \delta}{16} ≥ 16 α + β + γ + δ 1 α − 1 + β − 1 + γ − 1 + δ − 1 \frac{1}{\alpha^{-1} + \beta^{-1} + \gamma^{-1} + \delta^{-1}} α − 1 + β − 1 + γ − 1 + δ − 1 1 1 α β γ δ \frac{1}{\alpha\beta\gamma\delta} α β γ δ 1 Browse the problem library