Let's consider how logarithms work. When taking the logarithm of something, we can undo exponents.
log a^m = m log a
This is why it does not make any sense solving equations such as 56=x^8 with logarithms.
log x^8 = 8 log x
As we can see, x is in the argument of the logarithms which means it is not solved for. However, when the equation is 2=1.04^x, we can use logarithms to isolate x.
log 1.04^x = x log 1.04
Here we see that the variable is in the base of the power. This kind of equation we solve using radicals.
