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JEE Main

Exam: JEE Main
Subject: Mathematics
Chapter: Basics of Mathematics

JEE Main · Mathematics · Basics of Mathematics

If 2=a, 3=b, 7=c and 6^x=7^ x+4 then x is equal to

If

\log 2=a, \log 3=b, \log 7=c

and

6^x=7^{x+4}

then

x

is equal to

Options

A $\frac{4 b}{c+a-b}$
B $\frac{4 c}{a+b-c}$
C $\frac{4 c}{c-a-b}$
D $\frac{4 a}{a+b-c}$

Correct answer

B. $\frac{4 c}{a+b-c}$

Step-by-step solution

We have,

\begin{array}{cc}& 6^x=7^{x+4} \\ \Rightarrow & x \log 6=(x+4) \log 7 \\ \Rightarrow & x(\log 2+\log 3)=x \log 7+4 \log 7 \\ \Rightarrow & x(\log 2+\log 3-\log 7)=4 \log 7 \\ \Rightarrow & x=\frac{4 \log 7}{\log 2+\log 3-\log 7}=\frac{4 c}{a+b-c} \end{array}

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