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Solve for aa: 11a=71111^a=\frac{7}{\sqrt{11}}

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Full solution

Q. Solve for aa: 11a=71111^a=\frac{7}{\sqrt{11}}
  1. Identify and Simplify Equation: Identify the equation and simplify the right-hand side. 11a=71111^a = \frac{7}{\sqrt{11}} Multiply both sides by 11\sqrt{11} to clear the denominator. 11a⋅11=711^a \cdot \sqrt{11} = 7
  2. Clear Denominator by Multiplication: Simplify the left-hand side using properties of exponents. 11a×1112=11a+12=711^a \times 11^{\frac{1}{2}} = 11^{a + \frac{1}{2}} = 7
  3. Simplify Left-hand Side: Solve for 'a' by equating the exponents of base 1111. \newlinea+12=log⁡11(7)a + \frac{1}{2} = \log_{11}(7)\newlinea=log⁡11(7)−12a = \log_{11}(7) - \frac{1}{2}

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