Find the positive solution of the equation. \[ 2 x^{\frac{6}{7}}+12=524300 \] Answer Attempt 2 out of 2

To solve the equation \( 2 x^{\frac{6}{7}} + 12 = 524300 \), first, subtract 12 from both sides: \[ 2 x^{\frac{6}{7}} = 524300 - 12 \] \[ 2 x^{\frac{6}{7}} = 524288 \] Next, divide both sides by 2: \[ x^{\frac{6}{7}} = \frac{524288}{2} \] \[ x^{\frac{6}{7}} = 262144 \] Now, raise both sides to the power of \( \frac{7}{6} \): \[ x = (262144)^{\frac{7}{6}} \] Calculating \( 262144 = 2^{18} \), so \[ (262144)^{\frac{7}{6}} = (2^{18})^{\frac{7}{6}} = 2^{18 \cdot \frac{7}{6}} = 2^{21} \] Thus, the solution is: \[ x = 2^{21} = 2097152 \] Hence, the positive solution of the equation is \( x = 2097152 \).