`(log)_4 18` is

Options

A. a rational number
B. an irrational number
C. a prime number
D. none of these

Answer

B

Explanation

Let ` log_(4) 18 = p//q," where "p,q in I`
` rArr log_(4) 9+log_(4) 2 = p/q`
` rArr 1/2 xx 2 log _(2) 3 + 1/2 = p/q`
`rArr log_(2) 3 = p/q - 1/2 = m/n(say)`
where m, n` in I and n ne 0`
` rArr 3 = (2) ^(m//n)`
` or 3^(n) = 2^(m) ` (possible when m=n = 0 which is not true)
Hence, ` log_(4) 18` is an irrational number.