The value of x satisfying
`x+log_10(1+2^x)=x log_10 5+log_10 6` is

Answer

1

Explanation

` x + log_(10)(2^(x)+1)=x log_(10)5+log_(10)6`
` or x (log_(10)10-log_(10)5)+log_(10)(2^(x)+1)=log_(10)6`
` or x log_(10)2+log_(10)(2^(x)+1) = log_(10)6`
` or log_(10)2^(x) (2^(x)+1)=log_(10)6`
` or 2^(2x) + 2 ^(x) - 6 = 0`
` or (2^(x)+3)(2^(x)-2) = 0`
` :. 2^(x) =2`
` rArr x= 1`