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Operations on Rational and Irrational Numbers

Solve 5x ·√...

Question

Solve $5^{x} \cdot \sqrt[x]{8^{x - 1}} = 500$

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Solution

$5^{x} . \sqrt[x]{8^{x - 1}} = 500$
$5^{x} {.2}^{\frac{3 x - 3}{x}} = 5^{3} {.2}^{2}$
$\frac{3 x - 3}{x} = 2 ⟹ x = 3$

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Similar questions

Q. Solve the equation

5^{x} \sqrt[x]{8^{x - 1}} = 500

find the rational root .

2 x^{2} + 5 x - 1 + 8 x + x^{2} + 7 - 6 x + 3 - 3 x^{2}

x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8}

x + 7 - \frac{8 x}{3} = \frac{17}{6} - \frac{5 x}{2}

Q. Solve linear equation:

x + 7 - \frac{8 x}{3} = \frac{17}{6} - \frac{5 x}{2}

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