1) True/false: For any real number x,

Question

ln e^x = x.
I think that is true.

2)true/false:
(2 ln x)/ ln 10 = ln x^2 - ln 10 for all positive x.
I think this is true too.

Answer 1

1) True. That's the definition of the natural log.

2) No.
ln(x^2/10) = 2lnx - ln 10

That's not the same as 2lnx/ln10

ln x²/ln 10 = log₁₀x^2