$(0.16)^{\log _{2.5}\left(\frac{1}{3}+\frac{1}{3^{2}}+\frac{1}{3^{3}}+\ldots . to \infty\right)}$ ની કિમત શોધો
JEE MAIN 2020, Difficult
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d
\((0.16)^{\log _{2.5}\left(\frac{1}{3}+\frac{1}{3^{2}}+\ldots \ldots \ldots .+0 \infty\right)}\)
\((0.16)^{\log _{2.5}\left(\frac{1}{3}+\frac{1}{3^{2}}+\ldots \ldots \ldots .+0 \infty\right)}\)
\(=\left(\frac{4}{25}\right)^{\log _{\left(\frac{5}{2}\right)}\left(\frac{1}{2}\right)}\)
\(=\left(\frac{1}{2}\right)^{\log _{\left(\frac{5}{2}\right)}\left(\frac{4}{25}\right)}=\left(\frac{1}{2}\right)^{-2}=4\)
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