Question

Rezolvati in R ecuatia logaritm baza 2 din din x + logaritm baza x din 2 = 2

Answer 1

$log_{2}(x) + log_{x}(2) = 2$

$log_{2}(x) + \frac{1}{ log_{2}(x) } = 2$

$log_{2}(x) = t, \: t > 0$

$t + \frac{1}{t} = 2$

$t + \frac{1}{t} - 2 = 0 \: | \times t$

${t}^{2} + 1 - 2t = 0$

${t}^{2} - 2t + 1 = 0$

${(t - 1)}^{2} = 0$

$t - 1 = 0 = > t = 1$

$log_{2}(x) = 1 = > x = 2$