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Basic of Logarithms
medium
यदि $3^x=4^{x-1}$, तब $x=$
$(A)$ $\frac{2 \log _3 2}{2 \log _3 2-1}$ $(B)$ $\frac{2}{2-\log _2 3}$ $(C)$ $\frac{1}{1-\log _4 3}$ $(D)$ $\frac{2 \log _2 3}{2 \log _2 3-1}$
A
$(A,C,D)$
B
$(A,B,D)$
C
$(A,B,C)$
D
$(B,C,D)$
(IIT-2013)
Solution
$3^x=4^{x-1} $
$x=(x-1) \log _3 4 $
$x\left(1-2 \log _3 2\right)=-2 \log _3 2 $
$x=\frac{2 \log _3 2}{2 \log _3 2-1} \quad\quad$ Ans. $(A)$
Again
$x \log _2 3=(x-1) \cdot 2 $
$x\left(\log _2 3-2\right)=-2 $
$x=\frac{2}{2-\log _2 3}\quad\quad$ Ans. $(B)$
$x=\frac{1}{1-\frac{1}{2} \log _2 3}=\frac{1}{1-\log _4 3}\quad\quad$ Ans.$(C)$
Standard 11
Mathematics
