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If $\log 2 = a, \log 3 = b, \log 7 = c and 6^{x} = 7^{x + 4} then x =$

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

$\frac{4 b}{c - a - b}$

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

$\frac{4 b}{c + ab}$

answer is B.

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Detailed Solution

$\begin{array}{l} xlog 6 = (x + 4) \log 7 \Rightarrow x [a + b] = (x + 4) c \\ \Rightarrow x = \frac{4 c}{a + b - c} \end{array}$

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