Question

The value of $(0.05{)}_{\sqrt{20}}^{log}(0.1+0.01+0.001+.....)$

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

Answer 1

The correct option is A $81$

$(0.05{)}_{\sqrt{20}}^{log}(0.1+0.01+.....)=(\frac{1}{20}{)}^{2lo{g}_{20}\left(\frac{0.1}{1-0.1}\right)}={20}^{-2lo{g}_{20}\left(\frac{1}{9}\right)}={20}^{2lo{g}_{20}9}={20}^{lo{g}_{20}{9}^2}=9^2=81.$