Question

Me ajudem com logaritmo matemática

log4 0,1024 = x​

Answer 1

$\sf \: log_{4}(0.1024) = x \\ \\ \sf \: log_{2 {}^{2} }(0.1024) = x \\ \\ \sf \: log_{2 {}^{2} }\Bigg( \frac{64}{625} \Bigg) = x \\ \\ \sf \: log_{2 {}^{2} }\Bigg( \frac{8 {}^{2} }{625} \Bigg) = x\\ \\ \sf \: log_{2 {}^{2} }\Bigg( \frac{8 {}^{2} }{25 {}^{2} } \Bigg) = x \\ \\ \sf \: log_{2 {}^{2} }\Bigg(\Bigg( \frac{8}{25} \Bigg)\Bigg) {}^{2} = x \\ \\ \sf \: \frac{2}{2} \times log_{2}\Bigg( \frac{8}{25} \Bigg) = x \\ \\ \sf \: 1 log_{2}\Bigg( \frac{8}{25} \Bigg) = x\\ \\ \sf \: log_{2}\Bigg( \frac{8}{25} \Bigg) = x\\ \\ \sf \: log_{2}(8) - log_{2}(25) = x \\ \\ \sf \: log_{2}\Big(2 {}^{3} \Big) - log_{2}(25) = x \\ \\ \sf \: log_{2}\Big(2 {}^{3} \Big) - log_{2}\Big( {5}^{2} \Big) = x \\ \\ \sf \: 3 log_{2}(2) - log_{2}\Big(5 {}^{3} \Big) = x \\ \\ \sf \: 3 \times 1 - log_{2}\Big(5 {}^{3} \Big) = x\\ \\ \sf \: 1 - log_{2}\Big(5 {}^{3} \Big) = x \\ \\ \sf \: 3 - 2 log_{2}(5) = x \\ \\ \sf \: x = 3 - 2 log_{2}(5) \: ou \: x \approx \: - 1.64386$

Att: Nerd1990