Final answer:
The logarithmic form of the equation 6^2=36 is log_6 36 = 2, which corresponds to option a). This is found by using the definition of logarithms, where the base raised to the power of the logarithm equals the given number.
Step-by-step explanation:
The equation 6^2=36 can be converted into logarithmic form by following the definition of a logarithm. A logarithm can be understood as the operation of finding the exponent to which a base number must be raised to produce a given number. In other words, if we have an equation of the form b^x = y, it can be rewritten in logarithmic form as log_b(y) = x, where b is the base of the logarithm, y is the number we're taking the log of, and x is the exponent.
In the given equation, 6 is the base (b), 2 is the exponent (x), and 36 is the number (y). So, according to the definition of a logarithm, this can be rewritten as log_6(36) = 2. Hence, the correct logarithmic form of the equation 6^2=36 is option a) log_6 36 = 2