fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 12)
$${2^{2.322}} \cong 5\,\,\,\, \Rightarrow \,\,\,\,\,{\left( {{2^{2.322}}} \right)^{0.5}} = {5^{0.5}}\left( * \right)$$
$${{{2^{ - 5}} \cdot \root 3 \of {{{10}^2}} } \over {\root 6 \of {10} \cdot {2^x}}} = 1\,\,\,\, \Rightarrow \,\,\,{{\root 3 \of {{{10}^2}} } \over {\root 6 \of {10} }} = {{{2^x}} \over {{2^{ - 5}}}}$$
$$?\,\, \cong \,\,x\,\,$$
$${{\root 3 \of {{{10}^2}} } \over {\root 6 \of {10} }} = {{\root {3 \cdot 2} \of {{{10}^{2 \cdot 2}}} } \over {\root 6 \of {10} }} = \root 6 \of {{{10}^3}} = \sqrt {10} $$
$$\left. \matrix{
\sqrt {10} = {2^{0.5}} \cdot {5^{0.5}}\mathop = \limits^{\left( * \right)} {2^{0.5}} \cdot {2^{1.161}} = {2^{1.661}}\,\, \hfill \cr
{{{2^x}} \over {{2^{ - 5}}}} = {2^{x + 5}} \hfill \cr} \right\}\,\,\,\,\,\,\mathop \Rightarrow \limits^{2\, \ne \, - 1,0,1} \,\,\,\,x + 5 = 1.661\,\,\,\, \Rightarrow \,\,\,\,? = x = - 3.339$$
The correct answer is (B).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
