B3. Solve the equation $0.125 \cdot 4^{2 x-3}=\left(\frac{\sqrt{2}}{8}\right)^{-x}$.

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B3. We consider $0.125=2^{-3}, 4^{2 x-3}=2^{4 x-6}$ and $\left(\frac{\sqrt{2}}{8}\right)^{-x}=2^{\frac{5 x}{2}}$ and transform the equation: $2^{4 x-9}=2^{\frac{5 x}{2}}$. From this, we conclude $4 x-9=\frac{5 x}{2}$. The solution is $x=6$.

Consideration:

$0.125=2^{-3}$

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$4^{2 x-3}=2^{4 x-6}$

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and $\left(\frac{\sqrt{2}}{8}\right)^{-x}=2^{\frac{5 x}{2}}$

.1 point

Transforming the equation $2^{4 x-9}=2^{\frac{5 x}{2}}$ 1 point

Writing the equation $4 x-9=\frac{5 x}{2}$ 1 point

Solution of the equation $x=6$

1 point