Question

логарифмы решите 1 и 4

Answer 1

$1); ; lg2=a\\lg25=lg5^2=2cdot lg5=2cdot lgfrac{10}{2}=2cdot (lg10-lg2)=2cdot (1-a)\\2); ; log_{a}b=4\\log_{sqrt{ab}}Big (frac{sqrt{b}}{sqrt[4]{a}}Big )+log_{sqrt{ab}}(asqrt{a})=log_{sqrt{ab}}; frac{sqrt{b}cdot asqrt{a}}{sqrt[4]{a}}=log_{sqrt{ab}}; Big (b^{frac{1}{2}}cdot a^{frac{3}{2}-frac{1}{4}}Big )=\\=log_{sqrt{ab}}; b^{frac{1}{2}}+log_{sqrt{ab}}; a^{frac{5}{4}}=frac{1}{2}, log_{sqrt{ab}}; b+frac{5}{4}, log_{sqrt{ab}}; a=$

$=frac{1}{2}cdot frac{log_{a}b}{log_{a}sqrt{ab}}+frac{5}{4}cdot frac{log_{a}a}{log_{a}sqrt{ab}}=frac{1}{2}cdot frac{4}{log_{a}a^{frac{1}{2}}+log_{a}b^{frac{1}{2}}}+ frac{5}{4}cdot frac{1}{log_{a}a^{frac{1}{2}}+log_{a}b^{frac{1}{2}}}=\\=frac{2}{frac{1}{2}+frac{1}{2}cdot log_{a}b}+frac{5}{4}cdot frac{1}{frac{1}{2}+frac{1}{2}cdot log_{a}b}=frac{2}{frac{1}{2}(1+4)}+frac{5}{4}cdot frac{1}{frac{1}{2}(1+4)}=frac{4}{5}+frac{5}{4}cdot frac{2}{5}=$

$=frac{4}{5}+frac{1}{2}=frac{13}{10}=1,3$