Solve `(x+1)^(log_(10) (x+1))=100(x+1)`A. all the roots are positive real numbers.B. all the roots lie in the interval (0, 100)C. all the roots lie in the interval [-1, 99]D. none of these

Solve `(x+1)^(log_(10) (x+1))=100(x+1)`A. all the roots are positive r

1.	Solve `(x+1)^(log_(10) (x+1))=100(x+1)`A. all the roots are positive real numbers.B. all the roots lie in the interval (0, 100)C. all the roots lie in the interval [-1, 99]D. none of these
Answer» Correct Answer - C `(x+1)^(log_(10)(x+1))=100(x+1)` ` rArr log_(10) (x+1)^(log_(10)(x+1))=log_(10) (100(x+1))` ` rArr log_(10)(x+1)log_(10)(x+1) = 2 + log_(10) (x+1)` Let ` log_(10)(x+1) = y` ` rArr y^(2)-y-2=0` ` rArr y = 2 or - 1` ` rArr log_(10)(x+1) = 2, -1` ` rArr x+1 = 100, 1//10` ` rArr x =99 or - 9//10`