Question: The equation in exponential form. \[ \log_a 2 = \frac{3}{4} \] Options: 1. \(…

The equation in exponential form.

\[ \log_a 2 = \frac{3}{4} \]

Options:

1. \( a^{\frac{3}{4}} = 2 \)
2. \( 2^{\frac{3}{4}} = a \)
3. \( \left( \frac{3}{4} \right)^a = 2 \)
4. \( \frac{3}{4} = a^2 \)

Solution

The given equation is in logarithmic form: \[ \log_a 2 = \frac{3}{4} \] To convert it to exponential form, we need to rewrite it using the relationship between logarithms and exponents. This means saying that the base \( a \) raised to the exponent \(\frac{3}{4}\) is equal to 2. \[ a^{\frac{3}{4}} = 2 \] The correct choice is: \[ a^{\frac{3}{4}} = 2 \]