Odpowiedź:
x = 3
Szczegółowe wyjaśnienie:
[tex]log_{\sqrt{7}}(x^{3}-20) = 2\\\\Z: \ x^{3}-20 > 0\\x^{3} > 20[/tex]
Z def. logarytmu:
[tex]log_{a} b = c \ \ to \ \ a^{c} = b\\\\\sqrt{7}^{2} = x^{3}-20\\\\7 = x^{3}-20\\\\x^{3}-20 = 7\\\\x^{3} = 7+20\\\\x^{3} = 27\\\\x^{3} = 3^{3}\\\\\boxed{x = 3}[/tex]
Spr.
[tex]log_{\sqrt{7}}(3^{3}-20) = log_{\sqrt{7}}(27-20) = log_{\sqrt{7}}7 = log_{\sqrt{7}}\sqrt{7}^{2} = 2[/tex]
