Find the positive solution of the equation. 8x^((7)/(6))-8=2239480 Answer:

Isolate x term: First, we need to isolate the term with the variable x on one side of the equation. To do this, we add 8 to both sides of the equation to get rid of the -8 on the left side. 8x^(7/6) - 8 + 8 = 2239480 + 8 8x^(7/6) = 2239488Divide by 8: Next, we divide both sides of the equation by 8 to solve for x^(7/6). (8x^(7/6)) / 8 = 2239488 / 8 x^(7/6) = 279936Remove exponent: Now, we need to get rid of the exponent (7/6) to solve for x. We can do this by raising both sides of the equation to the reciprocal of (7/6), which is (6/7). (x^(7/6))^(6/7) = 279936^(6/7) x = 279936^(6/7)Simplify 279936^(6/7): We can simplify 279936^(6/7) by finding the 7th root of 279936 and then raising the result to the power of 6. The 7th root of 279936 is 18 because 18^7 = 279936. 18^(6) = 18 * 18 * 18 * 18 * 18 * 18Calculate x: Now we calculate 18 raised to the power of 6. 18^6 = 34012224 So, x = 34012224

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Q. Find the positive solution of the equation.

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8 x^{\frac{7}{6}}-8=2239480

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Answer:

Isolate x term: First, we need to isolate the term with the variable $x$ on one side of the equation. To do this, we add $8$ to both sides of the equation to get rid of the $-8$ on the left side. $\newline$ $8x^{(7/6)} - 8 + 8 = 2239480 + 8$ $\newline$ $8x^{(7/6)} = 2239488$
Divide by $8$ : Next, we divide both sides of the equation by $8$ to solve for $x^{\frac{7}{6}}$ . $\frac{8x^{\frac{7}{6}}}{8} = \frac{2239488}{8}$ $x^{\frac{7}{6}} = 279936$
Remove exponent: Now, we need to get rid of the exponent $(\frac{7}{6})$ to solve for $x$ . We can do this by raising both sides of the equation to the reciprocal of $(\frac{7}{6})$ , which is $(\frac{6}{7})$ . $\newline$ $(x^{(\frac{7}{6})})^{(\frac{6}{7})} = 279936^{(\frac{6}{7})}$ $\newline$ $x = 279936^{(\frac{6}{7})}$
Simplify $279936^{\frac{6}{7}}$ : We can simplify $279936^{\frac{6}{7}}$ by finding the $7$ th root of $279936$ and then raising the result to the power of $6$ . The $7$ th root of $279936$ is $18$ because $18^7 = 279936$ . $18^{6} = 18 \times 18 \times 18 \times 18 \times 18 \times 18$
Calculate $x$ : Now we calculate $18$ raised to the power of $6$ . $18^6 = 34012224$ So, $x = 34012224$