Oblicz: a)log₃81= b)log₇[latex] sqrt{7} [/latex]= c)log₂0.125= d)log₃3[latex]sqrt{3} [/latex]= e)log[latex] frac{1}{3} [/latex] 27 f)log₅[latex] frac{1}{25} [/latex] g)3log2-log 80+61log1= h)[latex] frac{6 ^{4} * 36 ^{-1} }{6 ^{-1} } [/latex] i)[

a) log₃81 = 4 ponieważ 3⁴ = 81 b) log₇√7 = 1/2 ponieważ 7¹/² = √7 c) log₂0,125 = log₂(1/8) = - 3 ponieważ 2⁻³ = (1/2)³ = 1/8 d) log₃3√3 = 3/2 ponieważ 3³/² = √3³ = √27 = 3√3 e) log₁/₃27 = - 3 ponieważ (1/3)⁻³ = 3³ = 27 f) log₅(1/25) = - 2 ponieważ 5⁻² = (1/5)² = 1/25 g) 3log2 - log80 + 61log1 = log2³ - log80 + log1⁶¹ = log8 - log80 + log1 =  = log(8/80) + log1 = log(1/10) + log1 = log(1/10) = - 1 ponieważ 10⁻¹ = 1/10 h) (6⁴ * 36⁻¹)/6⁻¹ = [6⁴ * (6²)⁻¹]/6⁻¹ = (6⁴ * 6⁻²)/6⁻¹ = 6⁴⁻²/6⁻¹ = 6²⁺¹ = 6³ = 216 i) √27/9 = 3√3/9 = √3/3 J) ∛16 * √2 * ⁴√8 = 16¹/³ * 2¹/² * 8¹/⁴ = (2⁴)¹/³ * 2¹/² * (2³)¹/⁴ = 2⁴/³ * 2¹/² * 2³/⁴ = = 2³¹/¹²