Question

UVUVIU
Value of logo
729
39x81
А
1
2
B
С.
co
2
2.​

Answer 1

Answer:

$\sqrt[4]{ \frac{729}{ \sqrt[3]{9 \times 81} } } = \sqrt[4]{ \frac{729}{ \sqrt[3]{9 \times 9 \times 9} } } = \sqrt[4]{ \frac{729}{9} } }$

$= \sqrt[4]{ \frac{729}{9} } } = \sqrt[4]{ \frac{81 \times 9}{9} } = \sqrt[4]{81}$

$= \sqrt[4]{81} = \sqrt[4]{3 \times 3 \times 3 \times 3} = 3$

$log_{9}\sqrt[4]{ \frac{729}{ \sqrt[3]{9 \times 81} } } = log_{9}(3) = \frac{ log(3) }{ log(9) }$

$\frac{ log(3) }{ log(9) } = \frac{ log(3) }{ log( {3}^{2} ) } = \frac{ log(3) }{ 2log(3) } = \frac{1}{2}$