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  4. The value of x satisfying 184 x-3=(54 √2)3 x-4 is

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Q. The value of $x$ satisfying $18^{4 x-3}=(54 \sqrt{2})^{3 x-4}$ is

Continuity and Differentiability

Solution:

$ 18^{4 x -3}=(54 \sqrt{2})^{3 x -4}$
Taking log on both sides
$ (4 x-3) \log 18=(3 x-4) \log 54 \sqrt{2} $
$\Rightarrow (4 x-3) \log 18=(3 x-4) \log (18)^{3 / 2} $
$\Rightarrow (4 x-3)=(3 x-4) \cdot \frac{3}{2} $
$\Rightarrow x=6$