If (4.2)^{x} = (0.42)^{y} = 100,then frac{1}{ | vedclass

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

Question

(C) Given $(4.2)^{x} = 100$ and $(0.42)^{y} = 100$.From $(4.2)^{x} = 100$,we have $4.2 = 100^{1/x} = (10^2)^{1/x} = 10^{2/x}$.From $(0.42)^{y} = 100$,

Vedclass · Accepted Answer

$1/2$

Vedclass · Answer

(C) Given $(4.2)^{x} = 100$ and $(0.42)^{y} = 100$.From $(4.2)^{x} = 100$,we have $4.2 = 100^{1/x} = (10^2)^{1/x} = 10^{2/x}$.From $(0.42)^{y} = 100$,we have $0.42 = 100^{1/y} = (10^2)^{1/y} = 10^{2/y}$.We know that $4.2 / 0.42 = 10$.Substituting the values,we get $10^{2/x} / 10^{2/y} = 10^1$.Using the laws of exponents,$10^{(2/x - 2/y)} = 10^1$.Equating the exponents,$2/x - 2/y = 1$.Dividing by $2$,we get $\frac{1}{x} - \frac{1}{y} = \frac{1}{2}$.

If $(4.2)^{x} = (0.42)^{y} = 100$,then $\frac{1}{x} - \frac{1}{y} = $

Similar Questions

If $\log 2 = 0.30103$ and $\log 3 = 0.4771$,then the number of digits in $(648)^{5}$ is

If $4^{x} + 2^{2x-1} = 3^{x+\frac{1}{2}} + 3^{x-\frac{1}{2}},$ then $x =$

If $\frac{\log _{2} x}{3}=\frac{\log _{2} y}{4}=\frac{\log _{2} z}{5 k}$ and $\frac{z}{x^{3} y^{4}}=1,$ then $k=$

If $\log _{10} 2986 = 3.4751$,then $\log _{10} 0.02986 =$

For $x>0,$ if $y=\frac{10^{\log _{10} x}}{x^{2}}$ and $x=y^{a},$ then $a=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module