1-log-1-6-x-2-3-log-1-6-3-

Question Number 95108 by bobhans last updated on 23/May/20

∣ 1 - \log_{(\frac{1}{6})} (x) ∣ + 2 = ∣ 3 - \log_{(\frac{1}{6})} (3) ∣

Answered by john santu last updated on 23/May/20

let 1 + \log_{6} (x) = t

∣ t ∣ + 2 = ∣ 2 + t ∣

t^{2} + 4 ∣ t ∣ + 4 = 4 + 4 t + t^{2}

∣ t ∣ - t = 0

case (1) t ⩾ 0 \Rightarrow t - t = 0, 0 = 0

always true, so t ⩾ 0 is solution

1 + \log_{6} (x) ⩾ 0 \Rightarrow \log_{6} (x) ⩾ - 1

x ⩾ \frac{1}{6} \Rightarrow solution x \in [\frac{1}{6}; + \infty)

Commented by bobhans last updated on 23/May/20

thank you

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