2015年5月2日 · Assuming $|x|<1$, if one can easily remember that $$ \dfrac{1}{1-x}=\sum_{n=0}^{\infty}x^{n} $$ then one can derive the following \begin{eqnarray*} \mbox{log}(1-x) & = & -\sum_{n=1}^{\...

ln(x) = log e (x) When e constant is the number: or . See: Natural logarithm. Inverse logarithm calculation. The inverse logarithm (or anti logarithm) is calculated by raising the base b to the logarithm y: x = log-1 (y) = b y. Logarithmic function. The logarithmic function has the basic form of: f (x) = log b (x) Logarithm rules

x^2: x^{\msquare} \log_{\msquare} \sqrt{\square} \nthroot[\msquare]{\square} \le \ge \frac{\msquare}{\msquare} \cdot \div: x^{\circ} \pi \left(\square\right)^{'} \frac{d}{dx} \frac{\partial}{\partial x} \int \int_{\msquare}^{\msquare} \lim \sum \infty \theta (f\:\circ\:g) f(x)

Free logarithm calculator - step-by-step solutions to help simplify logarithmic expressions.

2024年12月18日 · According to the reciprocal rule of logarithms, the logarithm of a number’s reciprocal (1 divided by that number) is equal to the negative of the logarithm of the original number. In mathematical notation: Formula: loga(1/X) = – loga(X) Example: loga(1/2) = – loga(2)

2021年1月13日 · If you accept (otherwise this can easily be proved) that $\log ()$ is a concave function, then it suffices to show (cf. Jensen) that $x$ is a tangent to $\log(1+x)$. But this is obvious: $x$ and $\log(1+x)$ touch at $x=0$ and have the same slope ($1$) there.

In other words, the logarithm of x, or logₐ(x), shows what power we need to raise a to (or if x is greater than 1, how many times a needs to be multiplied by itself) to produce the value x. From this view, we can represent the logarithm in the following way as well: a l o g a (x) = x \mathrm{a^{{log}_a(x)}} =\mathrm x a log a (x) = x

This free log calculator solves for the unknown portions of a logarithmic expression using base e, 2, 10, or any other desired base.

If you don't already know that $\log(x)=\int_1^x\frac1t\,dt$, one way to define the logarithm function is: $$\text{$\log(x)$ is the area under the curve $y=\frac1t$ from $t=1$ to $t=x$.}$$ The picture below shows that this area is sandwiched between two rectangles, each of width $x-1$.

2023年11月18日 · The lim x -> 0 (log(1 + x))/x formula is given by $\lim\limits_{x \to 0} \dfrac{\log(1+x)}{x}=1$. In this post, we will learn to prove the limit of log(1+x)/x when x tends to zero.