Question

what is the properties and formula of logarithms.​

Answer 1

HERE IS YOUR ANS

✨Definition

The logarithm of number b on the base a (loga b) is defined as an exponent, in which it is necessary raise number a to gain number b(The logarithm exists only at positive numbers). 

logab = x   if and only if   ax = b

✨The following types of logarithms are exist✨

loga b - logarithm of number b on the base a (a> 0, a ≠ 1, b > 0)

log b - common logarithms (Logarithms with base 10 are called common logarithms, a = 10).

ln b - natural logarithms (Logarithms with base e are called natural logarithms, a = e).


✨Formulas and properties of logarithms


For any a; a > 0; a ≠ 1 and any x; y > 0.

alogab = b

loga 1 = 0

loga a = 1

loga(x · y) = logax + logay

loga xy = logax - logay

loga 1x = -logax

loga xp = p logax

logak x = 1k loga x,    for k ≠ 0

logax = logac xc

loga x = logb xlogb a - change of base formula

loga x = 1logx a

☺️hope it helps you ☺️

Answer 2

. Logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. ... In the same fashion, since 102 = 100, then 2 = log10 100.