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

$\frac{2\log_{3}2}{2\log_{3}2-1}$

$\frac{2}{2-\log_{2}3}$

$\frac{1}{1-\log_{4}3}$

$\frac{2\log_{2}3}{2\log_{2}3-1}$

Option A,B,C

$3^{x}=4^{x-1}$ , taking log3on both sides

$\Rightarrow$ $x\log_3^3=(x-1)\log_3^4$

$\Rightarrow x=2 \log_3^2.x-\log_3^4$

$\Rightarrow$ $x(1-2\log_3^2)=-2\log_3^2$

$\Rightarrow$ $x=\frac{2\log_3^2}{2\log_3^2-1}$

$\Rightarrow x=\frac{1}{1-\frac{1}{2\log_3^2}}=\frac{1}{1-\frac{1}{\log_3^4}}=\frac{1}{1-\log_3^4}$

$\Rightarrow x=\frac{2}{2-\log_2^3}$

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