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If 2^8x=640000 : Multiple-choice Questions — Select One Answer Choice - Page 2

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If 2^8x=640000 [#permalink]
Fast approach:

Look at stem:
\(2^{2x-2}=\frac{2^x}{2}\)

We just need a value of \(2^x\)

\(2^{8x}=640,000=64*10^4\) -> splitting into 10^4 is convenient, because 8x divided by 4 gives us 2x (exponent rules)
\([2^{8x}]^{1/4}=[8^2*10^4]^{1/4}\)
\(2^{2x}=8^{1/2}*10\)
\(2^{2x}=2\sqrt{2}*10\)
\(2^{2x}=20\sqrt{2}\)

Now just divide that by 4, and you get:
\(\frac{2^{2x}}{4}=\frac{20\sqrt{2}}{4}=5\sqrt{2}\)

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If 2^8x=640000 [#permalink]
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