Question

The value of $(0.05)^{\log_{\sqrt{20}} ⥂ (0.1 + 0.01 + 0.001 + ......)}$ is

• A. 81
• B. $\frac{1}{81}$
• C. 20
• D. $\frac{1}{20}$

Answer 1

Answer: (A)

81

Answer 2

$(0.05)^{\log_{\sqrt{20}}(0.1 + 0.01 + ......)} = \left( \frac{1}{20} \right)^{2\log_{20}\left( \frac{0.1}{1 - 0.1} \right)}$

$= 20^{- 2\log_{20}(1/9)} = 20^{2\log_{20}9} = 20^{\log_{20}9^{2}} = 9^{2} = 81$.