If `log_a 3=1/3` then value of `a` is

Options

A. 27
B. 81
C. 72
D. none of these

Answer

To solve the equation \( \log_a 3 = \frac{1}{3} \), we will follow these steps:

### Step 1: Rewrite the logarithmic equation in exponential form
The equation \( \log_a 3 = \frac{1}{3} \) can be rewritten in exponential form. By the definition of logarithms, this means:
\[ a^{\frac{1}{3}} = 3 \]

### Step 2: Eliminate the fractional exponent
To eliminate the fractional exponent, we can raise both sides of the equation to the power of 3:
\[ (a^{\frac{1}{3}})^3 = 3^3 \]
This simplifies to:
\[ a = 27 \]

### Conclusion
Thus, the value of \( a \) is:
\[ \boxed{27} \]

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