I'm a bit confused on how to linearize an Exponential Graph

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I've seen other people answer questions on how to do this, I tried it and it didn't work. As of right now, I'm using the following desmos graphs.

Desmos, Exponential Graph

Desmos, Linearized Exponential Graph

I'm using $Y=ab^X$ as my exponential graph. I'm then using the least squares regression method, so:

$ln(Y)=ln(ab^X)$

$ln(Y)=ln(a)+X ln(b)$

Now that it's in form $Y=mX+b$, where $ln(Y)=Y, m=ln(b), b=ln(a)$. I then used the Least Square Regression Method, but the parameters in the line of best fit don't match up. Why not?

Linearized Graph with the parameters from the line of best fit

Exponential Graph with both lines of best fit

From what I understand the issue might be due to the fact that the data is not perfect.

Process for getting the values Math and values