If x = log_a(bc),y = log_b(ca),and z = log_c( | vedclass

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

Question

(B) Given $x = \log_a(bc)$,adding $1$ to both sides gives $1 + x = 1 + \log_a(bc) = \log_a(a) + \log_a(bc) = \log_a(abc)$.Taking the reciprocal,$(1 +

Vedclass · Accepted Answer

$(1 + x)^{-1} + (1 + y)^{-1} + (1 + z)^{-1}$

Vedclass · Answer

(B) Given $x = \log_a(bc)$,adding $1$ to both sides gives $1 + x = 1 + \log_a(bc) = \log_a(a) + \log_a(bc) = \log_a(abc)$.Taking the reciprocal,$(1 + x)^{-1} = \frac{1}{\log_a(abc)} = \log_{abc}(a)$.Similarly,$(1 + y)^{-1} = \log_{abc}(b)$ and $(1 + z)^{-1} = \log_{abc}(c)$.Adding these expressions,we get $(1 + x)^{-1} + (1 + y)^{-1} + (1 + z)^{-1} = \log_{abc}(a) + \log_{abc}(b) + \log_{abc}(c)$.Using the property $\log_n(m) + \log_n(p) = \log_n(mp)$,we have $\log_{abc}(a 	imes b 	imes c) = \log_{abc}(abc) = 1$.

If $x = \log_a(bc)$,$y = \log_b(ca)$,and $z = \log_c(ab)$,then which of the following is equal to $1$?

Similar Questions

If $\log 2=a, \log 3=b, \log 7=c$ and $6^x=7^{x+4}$, then $x$ is equal to:

The number of integers satisfying the inequality $\sqrt {{{\log }_3}(x) - 1} + \frac{{\frac{1}{2}{{\log }_3}({x^3})}}{{{{\log }_3}(\frac{1}{3})}} + 2 > 0$ is

The number of solutions of the equation $\log _{4}(x-1)=\log _{2}(x-3)$ is

$\log_{7} \log_{7} \sqrt{7 \sqrt{7 \sqrt{7}}} = ?$

If $\log x : \log y : \log z = (y - z) : (z - x) : (x - y)$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module