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y = ln x.

e^y = x,

dy/dx * e^y = 1,

dy/dx * x = 1,

dy/dx = 1/x.

My question is, why can't we use a similar method to prove the derivative of log(b)x = 1/x, like this:

y = log(b) x.

b^y = x,

dy/dx * b^y = 1,

dy/dx * x = 1,

dy/dx = 1/x.

Thanks so much everyone.