If 5 is approximately equal to 2^(2.322), which of the following is cl

\({2^{2.322}} \cong 5\,\,\,\, \Rightarrow \,\,\,\,\,{\left( {{2^{2.322}}} \right)^{0.5}} = {5^{0.5}}\left( * \right)\)

\({{{2^{ - 5}} \cdot \root 3 \of {{{10}^2}} } \over {\root 6 \of {10} \cdot {2^x}}} = 1\,\,\,\,\, \Rightarrow \,\,\,\,{{\root 3 \of {{{10}^2}} } \over {\root 6 \of {10} }} = {{{2^x}} \over {{2^{ - 5}}}}\)

\(?\,\, \cong \,\,x\,\,\)


\({{\root 3 \of {{{10}^2}} } \over {\root 6 \of {10} }} = {{\root {3 \cdot 2} \of {{{10}^{2 \cdot 2}}} } \over {\root 6 \of {10} }} = \root 6 \of {{{10}^3}} = \sqrt {10}\)

\(\left. \matrix{\\
{{{2^x}} \over {{2^{ - 5}}}} = {2^{x + 5}} \hfill \cr \\
\sqrt {10} = {2^{0.5}} \cdot {5^{0.5}}\mathop = \limits^{\left( * \right)} {2^{0.5}} \cdot {2^{1.161}} = {2^{1.661}}\,\, \hfill \cr} \right\}\,\,\,\,\,\,\mathop \Rightarrow \limits^{2\, \ne \, - 1,0,1} \,\,\,\,x + 5 = 1.661\,\,\,\, \Rightarrow \,\,\,\,? = x = - 3.339\)


The correct answer is (B).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.