1. [latex]log_3 189-log_3 7 = log_3 frac{189}{7} = log_3 27 = log_3 3^3 = 3 cdot log_3 3 = 3 cdot 1 = 3[/latex] 2. [latex]log_x 6 = -1[/latex] Zał. x > 0 i x ≠ 1 [latex]log_x 6 = -1[/latex] [latex]x^{- 1} = 6[/latex] [latex]x^{- 1} = 6^1[/latex] [latex]x^{- 1} = (frac{1}{6})^{-1}[/latex] [latex]x = frac{1}{6}[/latex] 3. [latex]log_{frac{1}{3}} (1-2x) = -2[/latex] Zał. 1 - 2x > 0 - 2x > - 1 /:(- 2) x < ½ [latex](frac{1}{3})^{-2} = 1-2x[/latex] [latex]3^2 = 1-2x[/latex] [latex]1-2x = 9[/latex] [latex]-2x = 9 - 1[/latex] [latex]-2x = 8 /:(- 2)[/latex] [latex]x = - 4[/latex] 4. [latex]log_4(log_3(log_2 x))=0[/latex] [latex]4^0 = log_3(log_2 x)[/latex] [latex]log_3(log_2 x) = 1[/latex] [latex]3^1 = log_2 x[/latex] [latex]log_2 x = 3[/latex] [latex]2^3 = x[/latex] [latex]x = 8[/latex]
