Question

Hi all, I'm on lecture 6 (file:///home/val/Desktop/18-01-fall-2006/contents/lecture-notes/lec6.pdf)

What I don't understand is on p.4:
If y = e^x, then ln(y) = x // that's fine

But then comes
If w = ln(x), then e^x = w

Shouldn't it be e^w = x ?

Thanks.

Answer 1

I would say yes. I haven't looked at the problem but:
\[\ln(x) = w => \log _{e}(x) = w => e^w=x\]

Answer 2

Yep, it's a misprint. Good catch @valk. And good explanation by @jkristia showing that ln is log base e.

A few lines below the misprint, they then restate the problem when calculating the derivative, dw/dx of w = ln(x). This time, the notes correctly takes the exponent on both sides giving \[e ^{w} = x\]


See attached image.