Question

Simplify: $\frac{1}{2^{{\log }_{1/2}2008}}$

Answer 1

Let$\frac{1}{2^{lo{g}_{1/2}}2008}=x$

$2^{-lo{g}_{1/2}2008}=x$

$2^{\frac{-log2008}{-log2}}=x$

$2^{\frac{log2008}{log2}}=x$

$2^{lo{g}_{2}2008}=x$

taking log on boyhside

$lo{g}_{2}2008lo{g}_{2}2=lo{g}_{2}x$

$lo{g}_{2}2008=lo{g}_{2}x$

$x=2008$