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$5^a = \sqrt{5}$ solve for $a$

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Solve equations with variable exponents

Full solution

Q.

5^a = \sqrt{5}

solve for

a

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

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