[latex]log_{a}b = c to a^{c} = b[/latex] [latex]a)\log_{x}81 = 4\\x^{4} = 81\\x^{4} = 3^{4}\\x = 3[/latex] [latex]b)\log_{2}x = 3\\x = 2^{3}\\x = 8[/latex] [latex]c)\log_{256}4 = x\\256^{x} = 4\\(4^{4})^{x} = 4^{1}\\4^{4x} = 4^{1}\\4x = 1 /:4\\x = frac{1}{4}[/latex] [latex]d)\log_{125}frac{1}{5} = x\\125^{x} = frac{1}{5}\\(5^{3})^{x} = 5^{-1}\\5^{3x} = 5^{-1}\\3x = -1 /:3\\x = -frac{1}{3}[/latex]
logₐb = x ===> aˣ = b a) logₓ 81 = 4 x⁴ = 81 x = ⁴√81 x = 3 log₃81 = 4 b) log₂ x = 3 x = 2³ x = 8 log₂8 = 3 c) log₂₅₆ 4 = x 256ˣ = 4 256¹/⁴ = 4 (⁴√256)¹ = 4 log₂₅₆4 = 1/4 d) log₁₂₅ 1/5 = x 125ˣ = 1/5 125⁻¹/³ = 1/5 (125)⁻¹/³ = (1/125)¹/³ = (∛1/125)¹ = 1/5 log₁₂₅1/5 = -1/3 Pozdrawiam
Pilne!! :) Oblicz: [latex]log_{4}256=[/latex] [latex]log_{3}frac{1}{27}=[/latex] [latex]log_{125}5=[/latex] [latex]logfrac{1}{100}=[/latex] Prosze wytłumaczcie mi to jak to się robi pokolei, bo nie mogę sobie przypomnieć. Z góry ...
Pojęcie logarytmu Oblicz: [latex] a)log_{3}81 \ b) log_{8}64 \ c) log_{5}125 \ d) log_{20}400 \ e) log_{3} 729 \ f) log_{4} 256 \ g) log_{2} frac{1}{32} \ h) log_{5} frac{1}{125} \ i) log_{8} 0,125 \ j) log_{5} 0,008[/latex]...
