log418=log4log18=2log2log2+log9=2log2log2+2log3=2log2log2+2log22log3=21+log23Since log23 is irrationalHence =21+log23 is irrational. Thereforelog418 is irrational number

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_{ 4 }{ 18 } is

Question

$lo g_{4} 18$ is

A rational number

An irrational number

A prime number

None of these

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Text solutionVerified

l o g_{4} 18 = \frac{l o g 18}{l o g 4}

= \frac{l o g 2 + l o g 9}{2 l o g 2}

= \frac{l o g 2 + 2 l o g 3}{2 l o g 2}

= \frac{l o g 2}{2 l o g 2} + \frac{2 l o g 3}{2 l o g 2}

= \frac{1}{2} + l o g_{2} 3

Since

l o g_{2} 3

is irrational

Hence

= \frac{1}{2} + l o g_{2} 3

is irrational.

Therefore

l o g_{4} 18

is irrational number

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Question Text	$lo g_{4} 18$ is
Answer Type	Text solution:1
Upvotes	150

log4​18 is

Text solutionVerified

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$lo g_{4} 18$ is