Find the positive solution of the equation. 2x^((6)/(7))-7=93305 Answer:

Add 7 to isolate variable: Add 7 to both sides of the equation to isolate the term with the variable. $2x^{\frac{6}{7}} - 7 + 7 = 93305 + 7$ $2x^{\frac{6}{7}} = 93312$Divide by 2: Divide both sides of the equation by 2 to solve for $x^{\frac{6}{7}}$. $\frac{2x^{\frac{6}{7}}}{2} = \frac{93312}{2}$ $x^{\frac{6}{7}} = 46656$Recognize perfect power: Recognize that 46656 is a perfect power of 6, specifically $6^6$. $46656 = 6^6$Use seventh root: Since $x^{\frac{6}{7}} = 6^6$, we can write $x$ as the seventh root of $6^6$ raised to the power of 6. $x = (6^6)^{\frac{7}{6}}$Simplify by multiplying exponents: Simplify the expression by multiplying the exponents. $x = 6^{6 \times \frac{7}{6}}$ $x = 6^7$Calculate final value: Calculate $6^7$ to find the value of $x$. $x = 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6$ $x = 279936$

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Q. Find the positive solution of the equation.

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2 x^{\frac{6}{7}}-7=93305

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Answer:

Add $7$ to isolate variable: Add $7$ to both sides of the equation to isolate the term with the variable. $\newline$ $2x^{\frac{6}{7}} - 7 + 7 = 93305 + 7$ $\newline$ $2x^{\frac{6}{7}} = 93312$
Divide by $2$ : Divide both sides of the equation by $2$ to solve for $x^{\frac{6}{7}}$ . $\newline$ $\frac{2x^{\frac{6}{7}}}{2} = \frac{93312}{2}$ $\newline$ $x^{\frac{6}{7}} = 46656$
Recognize perfect power: Recognize that $46656$ is a perfect power of $6$ , specifically $6^6$ . $\newline$ $46656 = 6^6$
Use seventh root: Since $x^{\frac{6}{7}} = 6^6$ , we can write $x$ as the seventh root of $6^6$ raised to the power of $6$ . $\newline$ $x = (6^6)^{\frac{7}{6}}$
Simplify by multiplying exponents: Simplify the expression by multiplying the exponents. $\newline$ $x = 6^{6 \times \frac{7}{6}}$ $\newline$ $x = 6^7$
Calculate final value: Calculate $6^7$ to find the value of $x$ . $\newline$ $x = 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6$ $\newline$ $x = 279936$