If \(2^x=3,\) then which of the following must be true?
A. \(1\frac13<x<1\frac12\)
B. \(1\frac12<x<1\frac23\)
C. \(1\frac23<x<1\frac34\)
D. \(1\frac34<x<1\frac56\)
E. \(1\frac56<x<2\)
Answer: B
Source: GMAT Club Tests
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If \(2^x=3,\) then which of the following must be true?
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Gmat_mission
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Solution:Gmat_mission wrote: ↑Tue Nov 10, 2020 7:28 amIf \(2^x=3,\) then which of the following must be true?
A. \(1\frac13<x<1\frac12\)
B. \(1\frac12<x<1\frac23\)
C. \(1\frac23<x<1\frac34\)
D. \(1\frac34<x<1\frac56\)
E. \(1\frac56<x<2\)
Answer: B
Source: GMAT Club Tests
Since 2^(3/2) = 2 * 2^(1/2) = 2√2 ≈ 2.8, we see that x > 3/2 since 2^x = 3 > 2.8.
Since 2^(5/3) = 2 * 2^(2/3) = 2∛4 ≈ 3.2, we see that x < 5/3 since 2^x = 3 < 3.2.
Therefore, we see that 3/2 < x < 5/3 or 1½ < x 1⅔.
Answer: B
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