2017年10月1日 · It does not matter what base we use providing the same base is used for all logarithms, here we are using bease e. Let us define A,B.C as follows=: A = ln a iff a = e^A , B …

2020年6月2日 · If a, b > 0 , then ln(ab)= lna + lnb. The author goes on to prove this theorem as follows. I do not understand what property allowed the author to use the substitution U = t/a …

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2016年11月6日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

2017年6月25日 · By definition: $$ x=\log_a b \quad \iff \quad a^x=b $$ and $$ a=e^{\ln a} \qquad b=e^{\ln b} $$ so: $$ a^x=b \quad \iff \quad \left(e^{\ln a}\right)^x=e^{x\ln a}=e^{\ln b} $$ and …

2022年11月16日 · Im reading the book: What Is Mathematics An Elementary Approach to IDEAS AND METHODS. There is a description before the proof of $\ln a + \ln b = \ln(ab)$ Intuitively, …

2023年10月5日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

2015年9月10日 · We use the fact that lna+lnb=lnab Hence we have that lnx+ln(x-2)=3=>ln(x(x-2))=3=> x(x-2)=e^3=> x^2-2x-e^3=0 The last is a trinomial with respect to x that has the …

2021年1月25日 · The $\impliedby$ at $(*)$ is justified by the fact that $\ln$ is an increasing function. The $\implies$ at $(*)$ is justified by the fact that $\exp$ is an increasing function. Share

I'm doing some Java code. As far as I can tell, Java only has functions that do natural log and base $10$ log. I have a requirement to specify the base. I've seen that doing $\ln x/ \ln b$ is …