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

Correct Answer is : 2log⁡322log⁡23−12₃ 2/2₂ 3 - 12log23−12log32

Correct Answer is : 2log⁡322log⁡23−12₃ 2/2₂ 3 - 12log23−12log32

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NIMCET 2016 Question Paper with solutions

Question : 80 of 120

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3^{x}

4^{x-1}

, then x =

Solution:

Given,

3^{x}=4^{x-1}

On taking log both sides, we get

\log(3^{x})=\log4^{(x-1)}

\Rightarrow x\log3=(x-1)\log4[\because \log m^{n}=n\log m]

\Rightarrow x\log3=x\log4-\log4

\Rightarrow x\log3-\log4=-\log4

\Rightarrow x(\log3-\log4)=-\log4

\Rightarrow -x(\log4-\log3)=-\log4

x=\frac{\log4}{\log4-\log3}

=\frac{\log2^{2}}{\log2^{2}-\log3}

=\frac{2\log2}{2\log2-\log3}

=\frac{\frac{2\log2}{\log3}}{\frac{2\log2-\log3}{\log3}}

[On dividing numerator and denominator by log 3]

\Rightarrow x=\frac{2\log_{3}2}{2\log_{3}2-1}

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