Basics Logarithms

About Euler: ln and figure e

ln = natural logarithm

log = decadal logarithm (with base 10)

e = 2.71828182845904523536028747135266……

 

How do you handle with e and ln (logarithmo naturalis)

some view essentials:

instead of e it is also written exp:

Examples:

exp(1) = 2.718281, exp(2) = 7.389056

ln(1) = 0, ln(2) = 0.693147

important Relations:

exp(ln(a)) = a

ln(exp(a)) = a

ln(a/b) = ln(a) – ln(b) = -ln(b/a)

ln(a*b) = ln(a) + ln(b)

aln(a) = ln(aexp(a)) example: 3ln(3) = ln(3exp3) or ln(3*3*3)

equation:

aexpx = b, x = lnb/lna

(read:  aexpx  =  a superscript x)

 

 

Multiplications and Divisions

 

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