Question

sqrt 8^x-3 = ^3sqrt 4^2-x

Answer 1

Answer on Question #47022 – Math – Algebra

sqrt 8^x-3 = ^3sqrt 4^2-x

Solution:

$$\sqrt{8^{x-3}} = \sqrt[3]{4^{2-x}}$$ $$8^{\frac{x-3}{2}} = 4^{\frac{2-x}{3}}$$ $$(2^3)^{\frac{x-3}{2}} = (2^2)^{\frac{2-x}{3}}$$ $$2^{\frac{3(x-3)}{2}} = 2^{\frac{2(2-x)}{3}}$$ $$\frac{3(x-3)}{2} = \frac{2(2-x)}{3}$$ $$9(x-3) = 4(2-x)$$ $$9x - 27 = 8 - 4x$$ $$13x = 35$$ $$x = \frac{35}{13}$$

Answer: $x = \frac{35}{13}$

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