Question

Is the Equation an Identity? Determine whether the given equation is an identity. If the equation is not an identity, find all its solutions.

$x{e}^{\ln x^2}=x^3$

Short answer

The given equation $x{e}^{\ln x^2}=x^3$is an identity.

Step-by-step solution

Step 1. Given information.

The given equation,$x{e}^{\ln x^2}=x^3$

Step 2. Simplify the given equation and verify it using suitable algebraic operations.

Given:$x{e}^{\ln x^2}=x^3$
Solve the given equation using property:$e^{\ln x}=x$

$\begin{array}{l}x{e}^{\ln x^2}=x^3\\ x\cdot x^2=x^3\\ x^3=x^3\end{array}$

LHS = RHS so the given equation is an identity