Question

log in baza √2 -1 din √3 +1 + log in baza √2 +1 din √3 +1 =
L-am încercat de 3 ori si nu mi-a ieșit . Menționez ca răspunsul trebuie sa dea 0 .

Answer 1

[tex]log_{\sqrt{2}-1}(\sqrt{3}+1)+log_{\sqrt{2}+1}(\sqrt{3}+1)=\\ =\frac{log_{\sqrt{3}+1}(\sqrt{3}+1)}{log_{\sqrt{3}+1}(\sqrt{2}-1)}+\frac{log_{\sqrt{3}+1}(\sqrt{3}+1)}{log_{\sqrt{3}+1}(\sqrt{2}+1)}=\\ =\frac{1}{log_{\sqrt{3}+1}(\sqrt{2}-1)}+\frac{1)}{log_{\sqrt{3}+1}(\sqrt{2}+1)}=\\[/tex]
[tex]=\frac{1}{log_{\sqrt{3}+1}(\sqrt{2}-1)}+\frac{1)}{log_{\sqrt{3}+1}(\sqrt{2}+1)}=\\ = \frac{log_{\sqrt{3}+1}(\sqrt{2}+1)+log_{\sqrt{3}+1}(\sqrt{2}-1)}{log_{\sqrt{3}+1}(\sqrt{2}+1)\cdot log_{\sqrt{3}+1}(\sqrt{2}-1)} =\\ [/tex]
[tex]= \frac{log_{\sqrt{3}+1}(\sqrt{2}+1)(\sqrt{2}-1)}{log_{\sqrt{3}+1}(\sqrt{2}+1)\cdot log_{\sqrt{3}+1}(\sqrt{2}-1)} =\\ =\frac{log_{\sqrt{3}+1}1}{log_{\sqrt{3}+1}(\sqrt{2}+1)\cdot log_{\sqrt{3}+1}(\sqrt{2}-1)} =\\ =\frac{0}{log_{\sqrt{3}+1}(\sqrt{2}+1)\cdot log_{\sqrt{3}+1}(\sqrt{2}-1)} =\\ =0 [/tex]