Solve the inequalities: a) e^2 < e^(x^2) < 3^16 b) ln(x − 1) − ln(x + 1) / 2 < 0 c. log2x > log3x

Question

****** c) log₂x > log₃x

Answer 1

In a, take ln of each term and work the algebra down to an expression with x in the middle.

In b, the expression really means x-1 < sqrt(x+1)...which means 1<x<3.

In c, 2x>3x which never happen for x>0 and log is not defined for x<0.