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

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GMATH Teacher
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Joined: 12 Oct 2010
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If 5 is approximately equal to 2^(2.322), which of the following is cl  [#permalink]

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17 Mar 2019, 11:55
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Difficulty:

45% (medium)

Question Stats:

58% (02:24) correct 42% (02:22) wrong based on 12 sessions

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GMATH practice exercise (Quant Class 12)

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Re: If 5 is approximately equal to 2^(2.322), which of the following is cl  [#permalink]

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17 Mar 2019, 16:53
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Solution attached.

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If 5 is approximately equal to 2^(2.322), which of the following is cl  [#permalink]

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17 Mar 2019, 18:05
fskilnik wrote:
GMATH practice exercise (Quant Class 12)

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

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

$$?\,\, \cong \,\,x\,\,$$

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

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

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

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: If 5 is approximately equal to 2^(2.322), which of the following is cl   [#permalink] 17 Mar 2019, 18:05
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