Why am I allowed to remove $\ln$ from both sides of an equation?
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 …
logarithms - Why is $\log_a (b)=\frac {\ln (b)} {\ln (a ...
Jun 25, 2017 · I know that formula, but I don't understand it. $\log_a (b)=\frac {\ln (b)} {\ln (a)}$ Thanks.
Show that $\ln (a+b) =\ ln (a) + \ln (b)$ when $a = \frac {b} {b-1}$
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 …
sequences and series - Show that $\ln n \lt 1+\frac {1} {2}+\cdots+ ...
5 days ago · 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 …
logarithms - How to solve if I have ln on both sides of equation ...
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
How to show that $n^ {\ln (\ln (n))} = \ln (n)^ {\ln (n)}$
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 …
Why are $\\log$ and $\\ln$ being used interchangeably?
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 …
Taylor Series for $\log (x)$ - Mathematics Stack Exchange
Nov 29, 2013 · Does anyone know a closed form expression for the Taylor series of the function $f(x) = \\log(x)$ where $\\log(x)$ denotes the natural logarithm function?
mathematical physics - What happen to units when we take Ln ...
Nov 7, 2020 · What happen to units when we take Ln? Ask Question Asked 5 years, 1 month ago Modified 1 year, 8 months ago
calculus - Power series representation of $\ln (1+x)
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 …