Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De differentiaal van log e . log x is gelijk aan [ log x = Briggse logaritme van x ]	A. $\large\boldsymbol{\frac 1x\,dx }$
	B. $\large\boldsymbol{\frac {\ln^210} {x}\,dx }$
	C. $\large\boldsymbol{\frac {1} {x\ln^210}\,dx}$
	D. $\large\boldsymbol{\frac {\log e^2} {x}\,dx }$
	E. $\boldsymbol{0 }$

[ 6-0894 - op net sinds 9.12.13-(E)-14.11.2024 ]

Translation in E N G L I S H

The differental of log e . log x is equal to	A. $\large\boldsymbol{\frac 1x\,dx }$
	B. $\large\boldsymbol{\frac {\ln^210} {x}\,dx }$
	C. $\large\boldsymbol{\frac {1} {x\ln^210}\,dx}$
	D. $\large\boldsymbol{\frac {\log e^2} {x}\,dx }$
	E. $\boldsymbol{0 }$

Oplossing - Solution

$\begin{aligned}&\text{Rekening houdend met}\;\log_a b=\frac{1}{\log_b a}\;\text{krijgen we}\\&d\,(\log e.\log x)=\log e.\,d\log x=\log e.\frac{1}{x.\ln 10}\;dx=\frac{1}{\ln 10}.\frac{1}{x.\ln 10}\;dx=\frac{1}{x.\ln^2 10}\;dx\end{aligned}$

De differentiaal van log e . log x is gelijk aan [ log x = Briggse logaritme van x ]	A. \(\large\boldsymbol{\frac 1x\,dx }\)
	B. \(\large\boldsymbol{\frac {\ln^210} {x}\,dx }\)
	C. \(\large\boldsymbol{\frac {1} {x\ln^210}\,dx}\)
	D. \(\large\boldsymbol{\frac {\log e^2} {x}\,dx }\)
	E. \(\boldsymbol{0 }\)

The differental of log e . log x is equal to	A. \(\large\boldsymbol{\frac 1x\,dx }\)
	B. \(\large\boldsymbol{\frac {\ln^210} {x}\,dx }\)
	C. \(\large\boldsymbol{\frac {1} {x\ln^210}\,dx}\)
	D. \(\large\boldsymbol{\frac {\log e^2} {x}\,dx }\)
	E. \(\boldsymbol{0 }\)