Jun 2, 2020 · My calculus book states the following theorem of the properties of natural logarithms: If a, b > 0 , then ln(ab)= lna + lnb The author goes on to prove this theorem as follows I do not understand...

Mar 17, 2019 · When I have this equation: $\ln (x+2) = \ln (x^2)$, why can I just remove the $\ln$ from both sides by raising it to the power of e. Does this not permanently change what the equitation equals?

May 23, 2019 · This can similarly be expressed as ln7 divided by ln4, using the natural logarithm. Using the above example, Why is it that these two ratios are equal, but log base 10 (7) is not equal to ln 7? …

Dec 18, 2025 · Now I know that $$\ln (1+n)<n\ \text {for}\ n\gt0$$ which implies that $$\ln n \lt n-1$$ Therefore every term in the series on the left must be less than its corresponding term in the …

Mar 6, 2016 · $$\ln \left (n^ {\ln\left (\ln (n)\right)}\right) = \ln \left ( \ln (n)^ {\ln (n)}\right)$$ Recall that $\log_b a^c = c\log_b a$. Use this property on both sides: $$\left (\ln\left (\ln (n)\right)\right)\left (\ln …

How to solve if I have ln on both sides of equation? Ask Question Asked 11 years, 7 months ago Modified 11 years, 7 months ago

The original question in my textbook asked if the equality $\ln (a+b) = \ln (a) + \ln (b)$ was true. My initial answer was that it was not true, but I missed this special case, which I think was very hard to "see".

Jun 25, 2017 · I know that formula, but I don't understand it. $\log_a (b)=\frac {\ln (b)} {\ln (a)}$ Thanks.

In some fields of engineering, $\log$ means $\log_ {10}$, in math it usually means $\ln$, and in computer science it often means $\log_2$ (when it matters). Another example of this kind of …

Nov 6, 2019 · I am reading an example in which the author is finding the power series representation of $\ln (1+x)$. Here is the parts related to the question: I think that I get everything except for one thing: ...