The value of y=0.36 \log _{0.25}(\frac{1}{3}+\frac{1}{3^{2}}+. . .) is

NIMCET 2008 Question Paper with solutions

Question : 12 of 120

Marks: +1, -0

The value of

y=0.36 \;\log _{0.25}(\;{1}/{3}+\;{1}/{3^{2}}+. . .)

Solution:

y=0.36 \log _{0.25}(\;{1}/{3}+\;{1}/{3^{2}}+. . .)

=0.36 \log _{0.25}(\;{1 {/ }3}/{1-\;{1}/{3}})=0.36 \log _{0.25} 1 {/ }2

=0.36 \log _{(1 {/ }2)^{2}}(1 {/ }2)

=\;{0.36}/{2} \log _{1 {/ }2}(1 {/ }2)

=0.36 × \;{1}/{2}=0.18

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