यदि `x+log_(15)(1+3^(x))=x log_(15)5+log_(15)12`, जब `x` एक पूर्णांक है, तो `x` किसके बराबर है ?

Options

A. -3
B. 2
C. 1
D. 3

Answer

C

Explanation

दिया है ,
` x + log_(15) (1 + 3^(x)) = x log_(15) 5 + log_(15) 12 `
` rArr log_(15) 15^(x) + log_(15) ( 1 + 3^(x)) = log _(15) 5^(x) log 15 ^(12) `
` [:' log_(b) a ^(m) = mlog_(b) a]`
` rArr log_(15) [15^(x)(1+3^(x))]= log_(15) (5^(x) xx 12) `
`[:' log a + log b = log ab]`
` 15^(x)(1+3^(x)) = 12 * 5^(x)`
` rArr 3^(x) (1+3^(x)) = 12 `
` rArr y(1+y) = 12 `
`[ "जहाँ " y = 3^(x)]`
` rArr y^(2) + y - 12 = 0`
` rArr (y+4)(y-3) = 0`
` rArr y = - 4,3`
` rArr 3^(x) = - 4,3`
` rArr 3^(x) = 3 " "[:' 3^(x) ne - 4]`
` rArr x= 1`