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# A.13: Logaritmos

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A continuación,$$x$$ y$$y$$ son números reales arbitrarios que son estrictamente mayores que 0,$$p$$ y$$q$$ son constantes arbitrarias que son estrictamente mayores que uno.

• $$q^{\log_q x}=x, \qquad \log_q \big(q^x\big)=x$$
• $$\log_q x=\frac{\log_p x}{\log_p q}$$
• $$\log_q 1=0, \qquad \log_q q=1$$
• $$\log_q(xy)=\log_q x+\log_q y$$
• $$\log_q\big(\frac{x}{y}\big)=\log_q x-\log_q y$$
• $$\log_q\big(\frac{1}{y}\big)=-\log_q y\text{,}$$
• $$\log_q(x^y)=y\log_q x$$
• $$\lim\limits_{x\rightarrow\infty}\log_q x=\infty, \qquad \lim\limits_{x\rightarrow0}\log_q x=-\infty$$
• La gráfica de$$\log_{10} x$$ se da a continuación. La gráfica de$$\log_q x\text{,}$$ para cualquiera$$q \gt 1\text{,}$$ es similar.

This page titled A.13: Logaritmos is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Joel Feldman, Andrew Rechnitzer and Elyse Yeager via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.