Difference between revisions of "What is Log"
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(Created page with "<math>(log_a x)= n </math>") |
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<math>(log_a x)= | |||
#First law If <math>log_a x = n </math> than <math>a^n = x </math> | |||
#Second law <math>log_n A + log_n B = log_(AB)</math> | |||
#Thirde law <math>log_A - log_B = log_({A \over B})</math> | |||
#law If "<math>{log_ x}^{log_ x} = {log_ x}^2 = n </math>" than "<math>{log_ x} = \sqrt[2]{n} </math>" | |||
#law if <math>log_ (x^n) = {log_ x}^n = n*{log_ x}</math> | |||
#law "<math>log_n (x) = {log_n (a)}</math>" than "x = a" | |||
<noinclude> | |||
==examples== | |||
====example 1==== | |||
ex1: <math>log_4 4 = n </math> find n. | |||
<math>log_a x = n </math> | |||
<math>a^n = x </math> | |||
<math>4^n = 4 </math> | |||
n=1 | |||
====example 2==== | |||
ex2: <math>log_4 x = 2 </math> find x. | |||
<math>log_a x = n </math> | |||
<math>a^n = x </math> | |||
<math>4^2 = x </math> | |||
x = 16 | |||
====example 3==== | |||
ex3: <math>log_a 25 =2 </math> find a. | |||
<math>log_a x = n </math> | |||
<math>a^n = x </math> | |||
<math>a^2 = 25 </math> | |||
a = 5 | |||
====example 4==== | |||
ex4: <math>log_a 25 =2 </math> find a. | |||
<math>log_a x = n </math> | |||
<math>a^n = x </math> | |||
<math>a^2 = 25 </math> | |||
a = 5 | |||
====example 5==== | |||
ex5: <math>log_4 x + log_4 (2x + 5)=2 </math> find x. | |||
#Second law <math>log_A + log_B = log_(AB)</math>. | |||
<math>log_4 x + log_4 (2x + 5)= log_4 (2x^2 + 4x) </math> | |||
<math>log_4 (2x^2 + 4x) = 2 </math> | |||
<math>4^2 = (2x^2 + 4x) </math> | |||
<math>2x^2 + 4x - 16 = 0</math> | |||
x= 2 and -4 | |||
====example 6==== | |||
ex6: <math>log_4 x + log_4 (x + 4) - log_4 (x^4 + 8x^3 + 16x^2) =2 </math> simplify | |||
<math>log_4 x + log_4 (x + 4) - log_4 (x^4 + 8x^3 + 16x^2) = 2</math> | |||
<math>log_4 x + log_4 (x + 4) = 2 + log_4 (x^4 + 8x^3 + 16x^2)</math> | |||
#Second law <math>log_n A + log_n B = log_(AB)</math> | |||
<math> log_4 x + log_4 (x + 4) = log_4 (x^2 + 4x)</math> | |||
<math> log_4 (x^2 + 4x) - log_4 (x^4 + 8x^3 + 16x^2) = 2 </math> | |||
#Thirde law <math>log_A - log_B = log_({A \over B})</math> | |||
<math>(x^2 + 4x) = 16(x^4 + 8x^3 + 16x^2) </math> | |||
<math> 16 (x^2 + 4)=0 </math> | |||
</noinclude> |
Latest revision as of 14:44, 6 October 2021
- First law If than
- Second law
- Thirde law
- law If "" than ""
- law if
- law "" than "x = a"
examples
example 1
ex1: find n.
n=1
example 2
ex2: find x.
x = 16
example 3
ex3: find a.
a = 5
example 4
ex4: find a.
a = 5
example 5
ex5: find x.
- Second law .
x= 2 and -4
example 6
ex6: simplify
- Second law
- Thirde law