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5a=55^a = \sqrt{5} solve for aa

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Full solution

Q. 5a=55^a = \sqrt{5} solve for aa
  1. Express in Same Base: We need to express both sides of the equation in terms of the same base to solve for 'aa'. The square root of 55 can be written as 55 raised to the power of 12\frac{1}{2}. So, we rewrite the equation as 5a=5125^a = 5^{\frac{1}{2}}.
  2. Set Exponents Equal: Since the bases are the same (both are 55), we can set the exponents equal to each other. This gives us the equation a=12a = \frac{1}{2}.
  3. Final Value of 'a': We have found the value of 'a' that satisfies the equation 5a=55^a = \sqrt{5}. There is no need for further calculation or simplification.

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