The value of (0.05)^{log_{sqrt{20}}(0.1 + 0.0 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $S = 0.1 + 0.01 + 0.001 + \dots$. This is an infinite geometric series with first term $a = 0.1$ and common ratio $r = 0.1$.$S = \frac{a}{1-r}

Vedclass · Accepted Answer

$81$

Vedclass · Answer

(A) Let $S = 0.1 + 0.01 + 0.001 + \dots$. This is an infinite geometric series with first term $a = 0.1$ and common ratio $r = 0.1$.$S = \frac{a}{1-r} = \frac{0.1}{1-0.1} = \frac{0.1}{0.9} = \frac{1}{9}$.Now,the expression is $(0.05)^{\log_{\sqrt{20}}(1/9)}$.Note that $0.05 = \frac{1}{20} = 20^{-1}$ and $\sqrt{20} = 20^{1/2}$.Using the property $\log_{a^n}(b) = \frac{1}{n} \log_a(b)$,we have $\log_{20^{1/2}}(1/9) = \frac{1}{1/2} \log_{20}(1/9) = 2 \log_{20}(1/9) = \log_{20}((1/9)^2) = \log_{20}(1/81)$.Thus,the expression becomes $20^{-1 \cdot \log_{20}(1/81)} = 20^{\log_{20}((1/81)^{-1})} = 20^{\log_{20}(81)} = 81$.

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

Similar Questions

Which of the following compound$(s)$ has '$Z$' configuration?

Production of a human protein in bacteria by genetic engineering is possible because

In which of the following reactions,the concentration of product is higher than the concentration of reactant at equilibrium? $(K = \text{equilibrium constant})$

In an astronomical telescope in normal adjustment,a straight black line of length $L$ is drawn on the inside part of the objective lens. The eyepiece forms a real image of this line. The length of this image is $I$. The magnification of the telescope is

Which of the following series of transition metal ions all have a $3d^2$ electronic configuration?

Vedclass Test Series

Exam Paper Generator

Online Exam Module