Final answer:
The equivalent logarithmic form of the equation 6^a = 137 is log6(137) = a. This uses the basic property of logarithms which states that the logarithm base b of x is equal to y when b raised to the power of y equals x.
Step-by-step explanation:
To convert the exponential equation 6^a = 137 to its equivalent logarithmic form, we apply the definition of a logarithm. The logarithmic form of this equation will express the exponent a as the logarithm of 137 with the base of 6. So, the equivalent logarithmic form of the given equation is log6(137) = a.
This is because the logarithm function is the inverse of the exponential function, meaning that logarithms allow us to bring down exponents to work with them more easily. In general, the relationship can be expressed as if b^y = x, then logb(x) = y. This is an application of the fundamental property of logarithms that relates exponential and logarithmic functions.