Basic Maths and Logarithm
Logarithmic Equations
IIT-JEE 2010 Paper 1
Grade 11
Question:
If $3^x = 4^{x-1}$, then $x$ equals:
(1) $\frac{2 \log_3 2}{2 \log_3 2 - 1}$
(2) $\frac{2}{2 - \log_2 3}$
(3) $\frac{1}{1 - \log_4 3}$
(4) $\frac{2 \log_2 3}{2 \log_2 3 - 1}$
Step-by-Step Solution
Key Concept: Take log: $x \log 3 = (x - 1) \log 4 \Rightarrow \log 4 = x(\log 4 - \log 3) \Rightarrow x = \frac{\log 4}{\log 4 - \log 3} = \frac{1}{1 - \log_4 3}$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)