Question

If $3^x=4^{x-1}$, then $x=$

• A. $\frac{2{\log }_{3}2}{2{\log }_{3}2-1}$
• B. $\frac{2}{2-{\log }_{2}3}$
• C. $\frac{1}{1-{\log }_{4}3}$
• D. $\frac{2{\log }_{2}3}{2{\log }_{2}3-1}$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $\frac{2{\log }_{3}2}{2{\log }_{3}2-1}$
B $\frac{2}{2-{\log }_{2}3}$
C $\frac{1}{1-{\log }_{4}3}$

$3^x=4^{x-1}$
$\Rightarrow {\log }_3{3}^x={\log }_3{4}^{x-1}$
$\Rightarrow x=(x-1){\log }_{3}4$
$\Rightarrow x=\frac{{\log }_{3}4}{{\log }_{3}4-1}$
$\Rightarrow x=\frac{2{\log }_{3}2}{2{\log }_{3}2-1}$
$\Rightarrow x=\frac{2}{2-{\log }_{2}3}$
$\Rightarrow x=\frac{1}{1-\frac{1}{2}{\log }_{2}3}$
$\Rightarrow x=\frac{1}{1-{\log }_{4}3}$