Question

if $5^a = \sqrt{5}$, what is the value of $a$ ?
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Explanation:

Step1: Rewrite the square root as an exponent

We know that $\sqrt{5}$ can be written as $5^{\frac{1}{2}}$ because the square root of a number is the same as raising that number to the power of $\frac{1}{2}$. So the equation $5^{a}=\sqrt{5}$ becomes $5^{a} = 5^{\frac{1}{2}}$.

Step2: Use the property of exponents

If we have two exponential expressions with the same base that are equal, i.e., $b^{x}=b^{y}$, then $x = y$ (where $b>0,b
eq1$). Here, the base $b = 5$, so we can set the exponents equal to each other. So $a=\frac{1}{2}$.

Answer:

$\frac{1}{2}$