If 3x-4x-1- then x-A- 2-lpg2B- 2108-2-2 log 3 2-1C- 1-log 4 3

The correct option is C 1/1 log_433^x = 4^x 1⇒ xlog 3 = 2 (x 1) log2 ⇒ x= 2log2/2log2 log3⇒ x = 2log_22/2log_22 log_23=2/2 log_23 Also x=1/1 1/2log_23= 1/1 lo ...

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Byju's Answer

Standard XII

Mathematics

Standard Formulae - 2

If 3x=4x-1, t...

Question

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

\frac{2 l o g_{3} 2}{2 l o g_{3} 2 - 1}

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\frac{2}{2 - l p g_{2} 3}

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\frac{1}{1 - l o g_{4} 3}

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\frac{2 l o g_{2} 3}{2 - l o g_{2} 3 - 1}

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Solution

The correct options are
A $\frac{2 l o g_{3} 2}{2 l o g_{3} 2 - 1}$
B $\frac{2}{2 - l p g_{2} 3}$
C $\frac{1}{1 - l o g_{4} 3}$
$3^{x} = 4^{x - 1} \Rightarrow x l o g 3 = 2 (x - 1) l o g 2 \Rightarrow x = \frac{2 l o g 2}{2 l o g 2 - l o g 3} \Rightarrow x = \frac{2 l o g_{2} 2}{2 l o g_{2} 2 - l o g_{2} 3} = \frac{2}{2 - l o g_{2} 3}$
Also $x = \frac{1}{1 - \frac{1}{2} l o g_{2} 3} = \frac{1}{1 - l o g_{4} 3}$

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