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Basic of Logarithms
hard
$(0.16)^{\log _{2.5}\left(\frac{1}{3}+\frac{1}{3^{2}}+\frac{1}{3^{3}}+\ldots . to \infty\right)}$ ની કિમત શોધો
A
$-4$
B
$2$
C
$-2$
D
$4$
(JEE MAIN-2020)
Solution
$(0.16)^{\log _{2.5}\left(\frac{1}{3}+\frac{1}{3^{2}}+\ldots \ldots \ldots .+0 \infty\right)}$
$=\left(\frac{4}{25}\right)^{\log _{\left(\frac{5}{2}\right)}\left(\frac{1}{2}\right)}$
$=\left(\frac{1}{2}\right)^{\log _{\left(\frac{5}{2}\right)}\left(\frac{4}{25}\right)}=\left(\frac{1}{2}\right)^{-2}=4$
Standard 11
Mathematics
