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Find the positive solution of the equation. 5x^((7)/(5))-27=10485733 Answer:

Find the positive solution of the equation.\newline5x75−27=10485733 5 x^{\frac{7}{5}}-27=10485733 \newlineAnswer:

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Full solution

Q. Find the positive solution of the equation.\newline5x75−27=10485733 5 x^{\frac{7}{5}}-27=10485733 \newlineAnswer:
  1. Add 2727 to both sides: Add 2727 to both sides of the equation to isolate the term with the variable on one side.\newline5x75−27+27=10485733+275x^{\frac{7}{5}} - 27 + 27 = 10485733 + 27
  2. Simplify both sides: Simplify both sides of the equation. 5x7/5=104857605x^{7/5} = 10485760
  3. Divide by 55: Divide both sides of the equation by 55 to solve for x75x^{\frac{7}{5}}.\newlinex75=104857605x^{\frac{7}{5}} = \frac{10485760}{5}
  4. Calculate division result: Calculate the division on the right side of the equation. x75=2097152x^{\frac{7}{5}} = 2097152
  5. Raise to power of 55/77: Raise both sides of the equation to the power of 5/75/7 to solve for xx.(x7/5)5/7=20971525/7(x^{7/5})^{5/7} = 2097152^{5/7}
  6. Simplify using exponent property: Simplify the left side of the equation using the property of exponents (am/n)n=am(a^{m/n})^n = a^m.x=20971525/7x = 2097152^{5/7}
  7. Calculate right side: Calculate the right side of the equation to find the value of xx.x≈2097152(5/7)x \approx 2097152^{(5/7)}
  8. Use calculator: Use a calculator to find the value of 20971525/72097152^{5/7}. x≈128x \approx 128

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