What does $\ln$ mean by itself?

Question

I have a few questions in my homework that as me to integrate $1 \over {3 + \ln - 2x}$ I thought $\ln$ was a function, why is it by itself? What does it mean?

Answer 1

By $~\ln x~$ or, $~\ln(x)~$ we mean logarithm of $~x~$ to the base $~e~$.

You can also say it as Natural Logarithm.

Definition: When $~e^y = x~$, then with respect to base $~e~$ logarithm of $~x~$ is $$\ln(x) = \log_e(x) = y$$The $~e~$, constant or Euler's number is: $~e ≈ 2.71828183~$.

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Your $~\dfrac{1}{3 + \ln - 2x}~$ is nothing but $~\dfrac{1}{3 + \ln(- 2x)}~$