solve-log-0-5-2-x-log-0-5-x-2-lt-0-

Question Number 172082 by Mikenice last updated on 23/Jun/22

s o l v e

{l o g}_{0.5}^{2} x + {l o g}_{0.5} x - 2 \underline{<} 0

Commented by mokys last updated on 23/Jun/22

{l o g}_{0.5}^{2} x + {l o g}_{0.5} x ⩽ 2

2 {l o g}_{0.5} x + {l o g}_{0.5} x ⩽ 2

3 {l o g}_{0.5} x ⩽ 2

{l o g}_{0.5} x ⩽ \frac{2}{3}

x ⩽ {(0.5)}^{\frac{2}{3}} ⩽ \sqrt[3]{\frac{1}{4}}

a n o t h e r w a y :

\frac{l n x}{l n (0.5)} ⩽ (\frac{2}{3}) \Rightarrow l n x ⩽ (\frac{2}{3}) l n (0.5)

l n x ⩽ l n {(0.5)}^{\frac{2}{3}} \Rightarrow x ⩽ {(0.5)}^{\frac{2}{3}} ⩽ \sqrt[3]{\frac{1}{4}}

A l d o l a i m y

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