Find the positive solution of the equation. 2x^((2)/(7))+19=147 Answer:

Isolate variable term: Isolate the term with the variable. Subtract 19 from both sides of the equation to isolate the term with the variable x. 2x^(2/7) + 19 - 19 = 147 - 19 2x^(2/7) = 128Subtract 19: Divide both sides by 2 to solve for x^(2/7). 2x^(2/7) / 2 = 128 / 2 x^(2/7) = 64Divide by 2: Raise both sides of the equation to the reciprocal of 2/7 to solve for x. (x^(2/7))^(7/2) = 64^(7/2) x = 64^(7/2)Raise to reciprocal: Simplify 64^(7/2). 64 is 2 raised to the 6th power (2^6), so we can rewrite 64^(7/2) as (2^6)^(7/2). x = (2^6)^(7/2) x = 2^(6 * 7/2) x = 2^21Simplify and calculate: Calculate 2^21. 2^21 is a large number, but since we are looking for a positive solution and we have not made any errors in our calculations, we can be confident that 2^21 is the correct answer.

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Q. Find the positive solution of the equation.

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2 x^{\frac{2}{7}}+19=147

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Answer:

Isolate variable term: Isolate the term with the variable. $\newline$ Subtract $19$ from both sides of the equation to isolate the term with the variable $x$ . $\newline$ $2x^{(2/7)} + 19 - 19 = 147 - 19$ $\newline$ $2x^{(2/7)} = 128$
Subtract $19$ : Divide both sides by $2$ to solve for $x^{\frac{2}{7}}$ . $\frac{2x^{\frac{2}{7}}}{2} = \frac{128}{2}$ $x^{\frac{2}{7}} = 64$
Divide by $2$ : Raise both sides of the equation to the reciprocal of $\frac{2}{7}$ to solve for $x$ . $\left(x^{\frac{2}{7}}\right)^{\frac{7}{2}} = 64^{\frac{7}{2}}$ \[$x = 64^{\frac{7}{2}}$]
Raise to reciprocal: Simplify $64^{\frac{7}{2}}$. $64$ is $2$ raised to the $6$th power $(2^6)$, so we can rewrite $64^{\frac{7}{2}}$ as $(2^6)^{\frac{7}{2}}$. $x = (2^6)^{\frac{7}{2}}$ $x = 2^{6 \cdot \frac{7}{2}}$ $x = 2^{21}$
Simplify and calculate: Calculate $2^{21}$. $2^{21}$ is a large number, but since we are looking for a positive solution and we have not made any errors in our calculations, we can be confident that $2^{21}$ is the correct answer.