[phpBB Debug] PHP Notice: in file /includes/db/mysqli.php on line 43: mysqli_connect() [function.mysqli-connect]: Headers and client library minor version mismatch. Headers:50545 Library:50636
[phpBB Debug] PHP Notice: in file /includes/session.php on line 1007: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3493)
[phpBB Debug] PHP Notice: in file /includes/session.php on line 1007: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3493)
[phpBB Debug] PHP Notice: in file /includes/session.php on line 1007: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3493)
[phpBB Debug] PHP Notice: in file /includes/functions.php on line 4284: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3493)
[phpBB Debug] PHP Notice: in file /includes/functions.php on line 4286: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3493)
[phpBB Debug] PHP Notice: in file /includes/functions.php on line 4287: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3493)
[phpBB Debug] PHP Notice: in file /includes/functions.php on line 4288: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3493)
 Logarytmy-wzory
Biuro Konstrukcji Elektronicznych






teraz jesteś Wzory
Logarytmy-wzory

 

Logarytmy-wzory

Logarytmem liczby b przy podstawie a nazywamy wykładnik potęgi, do której należy podnieść a, aby otrzymać liczbę b, przy założeniach, że a,\:b są liczbami dodatnimi oraz a \not{=} 1.
\log_a{b}\:=\:c \:\:\: \Leftrightarrow \:\:\: a^c=b
Szczególne przypadki: 
Logarytmem dziesiętnym nazywamy logarytm przy podstawie 10\log b\:=\:c \:\:\: \Leftrightarrow \:\:\: 10^c=b

Logarytmem naturalnym nazywamy logarytm przy podstawie e,
gdzie e \approx 2,71

\ln b\:=\:c \:\:\: \Leftrightarrow \:\:\: e^c=b
Własności:
\log_a 1\:=\:0\log_a (b \cdot c)\:=\: \log_a b \:+\: \log_a c
\log_a a\:=\: 1\log_a \frac{b}{c}\:=\: \log_a b \:-\: \log_a c
\log_a a^b\:=\: b\log_a b^n\:=\: n \cdot \log_a b
a^{\log_a b}\:=\: b\log_a \sqrt[n]{b}\:=\: \frac{1}{n} \cdot \log_a b

Zamiana podstaw logarytmu

\log_a b\:=\: \frac{\log_c b}{\log_c a}

cron