If {log _{10}}x = y,then {log _{1000}}{x^2} i | vedclass

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

Question

(D) Given that ${\log _{10}}x = y$. We need to evaluate ${\log _{1000}}{x^2}$. Using the change of base formula and properties of logarithms: ${\log _

Vedclass · Accepted Answer

$\frac{2y}{3}$

Vedclass · Answer

(D) Given that ${\log _{10}}x = y$. We need to evaluate ${\log _{1000}}{x^2}$. Using the change of base formula and properties of logarithms: ${\log _{1000}}{x^2} = \frac{{\log _{10}}{x^2}}{{\log _{10}}{1000}}$ $= \frac{2{\log _{10}}x}{{\log _{10}}{{10}^3}}$ $= \frac{2{\log _{10}}x}{3{\log _{10}}10}$ Since ${\log _{10}}10 = 1$,we have: $= \frac{2}{3}{\log _{10}}x = \frac{2}{3}y$.

If ${\log _{10}}x = y$,then ${\log _{1000}}{x^2}$ is equal to

Similar Questions

If $\log_2 x + \log_x 2 = \frac{10}{3} = \log_2 y + \log_y 2$ and $x \neq y$,then $x + y = $

What is the number of solutions for the equation $\log_4(x - 1) = \log_2(x - 3)$?

$7^{2 \log _{7} 5}$ is equal to

If $a, b, c \neq 0$ and belong to the set $\{0, 1, 2, 3, \ldots, 9\}$,then $\log _{10}\left(\frac{a+10 b+10^2 c}{10^{-4} a+10^{-3} b+10^{-2} c}\right)$ is equal to

What is the number of real values of the parameter $k$ for which the equation $({\log _{16}}x)^2 - {\log _{16}}x + {\log _{16}}k = 0$ has exactly one solution,given that the coefficients are real?

Vedclass Test Series

Exam Paper Generator

Online Exam Module