Question

ln 7x = ln (21x + 14)

Explanation:

Step1: Apply injectivity of ln function

If $\ln a = \ln b$, then $a = b$. So $7x = 21x + 14$.

Step2: Solve for x

Rearrange terms: $7x - 21x = 14$ → $-14x = 14$ → $x = -1$.

Step3: Check domain validity

$\ln(7x)$ requires $7x > 0$ → $x > 0$. $x=-1$ is invalid.

Answer:

No solution