Gujarati
Basic of Logarithms
medium

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

$(A)$ $\frac{2 \log _3 2}{2 \log _3 2-1}$ $(B)$ $\frac{2}{2-\log _2 3}$ $(C)$ $\frac{1}{1-\log _4 3}$ $(D)$ $\frac{2 \log _2 3}{2 \log _2 3-1}$

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

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