If a^x = b,b^y = c,and c^z = a,then the value | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given equations are $a^x = b$,$b^y = c$,and $c^z = a$.Taking the logarithm on both sides of each equation:$x = \log_a b$$y = \log_b c$$z = \log_c

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) Given equations are $a^x = b$,$b^y = c$,and $c^z = a$.Taking the logarithm on both sides of each equation:$x = \log_a b$$y = \log_b c$$z = \log_c a$Now,calculate the product $xyz$:$xyz = (\log_a b) 	imes (\log_b c) 	imes (\log_c a)$Using the change of base formula $\log_m n = \frac{\log n}{\log m}$:$xyz = \left(\frac{\log b}{\log a}ight) 	imes \left(\frac{\log c}{\log b}ight) 	imes \left(\frac{\log a}{\log c}ight)$Canceling the common terms in the numerator and denominator:$xyz = 1$.

If $a^x = b$,$b^y = c$,and $c^z = a$,then the value of $xyz$ is:

Similar Questions

Which phylum is characterized by the presence of a central cavity known as the spongocoel?

Name the blood cells,whose reduction in number can cause clotting disorder,leading to excessive loss of blood from the body.

What is the stored food material in fungi?

$A$ heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio $3: 1$. The ratio of radii of the fragments is

Mesoglea is

Vedclass Test Series

Exam Paper Generator

Online Exam Module