Oblicz: a) log₂1:1024 -> (1:1024 to ułamek) b)log₃243 c)log indeks dolny√5 5∛5 d)log indeks dolny ∛3 27 e)log₂8√2 f)log₃x=-1 g)log₅x=3 h)log½x=-2 i)logx25=2 j)logx81=4 k)logx3=½

a)log₂(1:1024) = log₂(1024)⁻¹ = log₂(2¹⁰)⁻¹ = log₂2⁻¹¹ = - 11 b)log₃(243) = log₃(3)⁵ = 5 c)[latex]log_{sqrt{5}}(5sqrt[3]{5}) = log_{sqrt{5}}(5cdot5^{frac{1}{3}}) = log_{sqrt{5}}(sqrt{5}^{2})^{frac{4}{3}} = log_{sqrt{5}}(sqrt{5})^{frac{8}{3}} = frac{8}{3}[/latex]  d)[latex]log_{sqrt[3]{3}}(27) = log_{sqrt[3]{3}}(sqrt[3]{3})^{9} = 9[/latex] e)[latex]log_{2}(8sqrt{2}) = log_{2}(2^{3}cdot2^{frac{1}{2}}) = log_{2}(2)^{frac{7}{2}} = frac{7}{2}[/latex]   f)log₃x=-1 x = 3⁻¹ = ⅓ g)log₅x=3 x = 5³ = 125 h)log½x=-2 x = ½⁻² = 4   i)logx25=2 x² = 25 x = 5 j)logx81=4 x⁴ = 81 x = 3 k)logx3=½ x^½ = 3 x = 9