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

Correct Answer is : 2log322log23−1

NIMCET 2016 Question Paper with solutions

Question : 80 of 120

Marks: +1, -0

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)}

⇒x\log3=(x-1)\log4[∵\logm^{n}=n\logm]

⇒x\log3=x\log4-\log4

⇒x\log3-\log4=-\log4

⇒x(\log3-\log4)=-\log4

⇒-x(\log4-\log3)=-\log4

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

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

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

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

[On dividing numerator and denominator by log 3]

⇒x={2\log_{3}2}/{2\log_{3}2-1}

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