JEE Advanced 2013 · Paper 2, Mathematics question 42

Solve. $x\ln3=(x-1)\ln4$, so $x=\dfrac{\ln4}{\ln4-\ln3}=\dfrac{2\ln2}{2\ln2-\ln3}$.

• (A) divide by $\ln3$: $\dfrac{2\log_32}{2\log_32-1}$ ✓
• (B) divide by $\ln2$: $\dfrac2{2-\log_23}$ ✓
• (C) divide by $\ln4$: $\dfrac1{1-\log_43}$ ✓
• (D) would need $\ln3$ and $\ln2$ swapped. ✗

(A), (B), (C)