The number $l o g_{20}$ 3 lies in

(\frac{1}{4}, \frac{1}{3})

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(\frac{1}{3}, \frac{1}{2})

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(\frac{1}{2}, \frac{3}{4})

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(\frac{3}{4}, \frac{4}{5})

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Solution

The correct option is B $(\frac{1}{3}, \frac{1}{2})$
$9 < 20 < 27$ or $3^{2} < 20 < 3^{3}$
$∴ 2 l o g 3 < l o g 20 < 3 l o g 3$
or $2 < \frac{l o g 20}{l o g 3} < 3 o r \frac{1}{2} > \frac{l o g 3}{l o g 20} > \frac{1}{3}$
or $\frac{1}{3} < l o g_{20} 3 < \frac{1}{2}$

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Similar questions

Q. Evaluate:

\frac{(3 \frac{2}{3})^{2} - (2 \frac{1}{2})^{2}}{(4 \frac{3}{2})^{2} - (3 \frac{1}{3})^{2}}

\div

\frac{3 \frac{2}{3} - 2 \frac{1}{2}}{4 \frac{3}{2} - 3 \frac{1}{3}}

Q. Simplify:

\frac{{(3 \frac{2}{3})}^{2} - {(2 \frac{1}{2})}^{2}}{{(4 \frac{3}{4})}^{2} - {(3 \frac{1}{3})}^{2}} \div \frac{3 \frac{2}{3} - 2 \frac{1}{2}}{4 \frac{3}{4} - 3 \frac{1}{3}}

Odd one out among the following numbers $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}$ is,

Two dice are thrown. The events P and Q are as follows:

P: getting an odd number on the first die.
Q: getting the sum of the numbers on the dice less than 5.
Then, P and Q is:

\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}

is a

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The number log20 3 lies in

The correct option is B (13,12)9<20<27 or 32<20<33 ∴ 2log3<log20<3log3 or 2<log20log3<3 or 12>log3log20>13 or 13<log20 3<12

The number $l o g_{20}$ 3 lies in

The correct option is B $(\frac{1}{3}, \frac{1}{2})$
$9 < 20 < 27$ or $3^{2} < 20 < 3^{3}$
$∴ 2 l o g 3 < l o g 20 < 3 l o g 3$
or $2 < \frac{l o g 20}{l o g 3} < 3 o r \frac{1}{2} > \frac{l o g 3}{l o g 20} > \frac{1}{3}$
or $\frac{1}{3} < l o g_{20} 3 < \frac{1}{2}$