Question

If a,b,c are positive real numbers ,then the value of (ab)^log(a/b) × (bc)^log(b/c)× (ca)^log(c/a) =
correct answer will be marked as brainliest
A)0
B)-1
C)1
D)none of this​

Answer 1

Step-by-step explanation:

Hope you understand

mark brainliest please

Answer 2

The correct answer is option (C) 1

Given:

a, b, c are positive real numbers

To find:

The value of  $[ab^{log (\frac{a}{b}) } ] [ bc^{log(\frac{b}{c} )} ] [ ca^{log (\frac{c}{a}) } ]$

Solution:

Let P = $[ab^{log (\frac{a}{b}) } ] [ bc^{log(\frac{b}{c} )} ] [ ca^{log (\frac{c}{a}) } ]$

apply ㏒ both sides

⇒ ㏒ P = ㏒ $[ab^{log (\frac{a}{b}) } ] [ bc^{log(\frac{b}{c} )} ] [ ca^{log (\frac{c}{a}) } ]$  

⇒ ㏒ P = ㏒ $[ab^{log (\frac{a}{b}) } ]$ + ㏒ $[ bc^{log(\frac{b}{c} )} ]$ + ㏒ $[ ca^{log (\frac{c}{a}) } ]$  

⇒ ㏒ P = ㏒ $(\frac{a}{b})$ ㏒ $(ab)$ + ㏒ $(\frac{b}{c} )$ ㏒ $(bc)$ +㏒ $(\frac{c}{a})$ ㏒ $(ca)$

⇒ ㏒ P = [㏒a - ㏒b][㏒a + ㏒b]+[㏒b - ㏒c][㏒b + ㏒c]+[㏒c - ㏒a][㏒c + ㏒a]  

⇒ ㏒ P = (㏒a)² - (㏒b)² + (㏒b)² - (㏒c)²+  (㏒c)²-  (㏒a)²  

⇒ ㏒ P = 0 =  ㏒ 1

⇒ P = 1  

The value of $[ab^{log (\frac{a}{b}) } ] [ bc^{log(\frac{b}{c} )} ] [ ca^{log (\frac{c}{a}) } ]$ is 1

#SPJ2