Question

Calculați.
E urgent.​

Answer 1

$\displaystyle log_aa\sqrt{a\sqrt{a\sqrt{a} } } =log_aa\sqrt{a\sqrt{a\cdot a^{\frac{1}{2} }}} } =log_aa\sqrt{a \sqrt{a^{1+\frac{1}{2} }} } =log_aa\sqrt{a\sqrt{a^{\frac{2+1}{2} }} } =\\\\=log_aa\sqrt{a\sqrt{a^{\frac{3}{2} }} } =log_aa\sqrt{a \cdot a^{\frac{3}{2}\cdot \frac{1}{2} }} =log_aa\sqrt{a \cdot a^{\frac{3}{4}} } =log_aa\sqrt{a^{1+\frac{3}{4} }}=$

$\displaystyle =log_aa\sqrt{a^{\frac{4+3}{4} }} =log_aa\sqrt{a^\frac{7}{4} }=log_aa^{1+\frac{7}{4} \cdot \frac{1}{2} } =log_aa^{1+\frac{7}{8}} =log_aa^{\frac{8+7}{8} }=\\\\ =log_aa^{\frac{15}{8} }=\frac{15}{8} \cdot 1=\frac{15}{8}$

Answer 2

$\it log_a a\cdot a^{\frac{1}{2}}\cdot a^{\frac{1}{4}}\cdot a^{\frac{1}{8}}=log_a a^{1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}}=log_a a^\frac{15}{8}=\dfrac{15}{8}log_aa=\dfrac{15}{8}$