Question

Rezolvati in R ecuatia ㏒₃x=㏒ₓ3.
Am facut ca ㏒₃x=1/log in baza 3 din x si mai incolo nu mi-a mai dat.

Answer 1

$log_{3}(x) = log_{x}(3)$

$log_{3}(x) = \frac{1}{ log_{3}(x) }$

$notam \: log_{3}(x) \: cu \: t.$

$log_{3}(x) = t \: \: ,t > 0$

$t = \frac{1}{t} = > {t}^{2} = 1 = > t = \pm \sqrt{1} = \pm1$

$= > t_{1} = - 1 \: nu \: convine$

$= > t_{2} = 1$

$log_{3}(x) = 1 = > x = 3$

$log_{3}(3) = 1$