I plugged '8^x+2^x=130, solve for x' into chatGPT as a test, after 1 minute it gave 3 methods to find a solution and a rough answer of 2.42. I asked it to use one of the other methods, which it said would be more accurate, and it has told me that using the bisection method we get 2.321928094
It then said that 8^2.321928094+2^2.321928094=128.000003218 + 1.999996782=130.000000
The first thing that jumped out at me is that 2^2.321928094 is closer to 5, and cannot be less than 2. I told ChatGPT this, and it then told me that the sum it gave me actually resolved out to 133 (also incorrect) and so the original equation was what was wrong and should have been 8^x+2^x=133. Hilarious, you couldn't make it up.
It turns out that when calculated properly:
8^2.321928094=124.99999976934773412728988276068
2^2.321928094=4.9999999969246364531389595814579
and their sum is 129.99999976627237058042884234214
So the answer it gave me, 2.321928094, was actually fairly accurate, but it completely failed when explaining why, then doubled down on its ignorance and incorrect maths and then decided that the wrong answer it gave must have been right and this meant the original question must have been wrong...