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If 5^(a)=sqrt5, what is the value of a ?

If 5a=5 5^{a}=\sqrt{5} , what is the value of a a ?

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Full solution

Q. If 5a=5 5^{a}=\sqrt{5} , what is the value of a a ?
  1. Express 5\sqrt{5}: First, we need to express 5\sqrt{5} in terms of 55 to the power of a fraction since any square root can be expressed as a power of 12\frac{1}{2}.\newlineCalculation: 5=512\sqrt{5} = 5^{\frac{1}{2}}
  2. Equation with same bases: Now, we have the equation 5a=5125^{a} = 5^{\frac{1}{2}}. Since the bases are the same, we can equate the exponents.\newlineCalculation: a=12a = \frac{1}{2}

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