Question

If y =${\log }_x$ 2. Find the value of ${\log }_4$ x.

• A. 2y
• B.
• C. y
• D. y²

Answer 1

The correct option is B

Given y =${\log }_x$ 2

${\log }_{4}x$ = ${\log }_{2^2}x$ = $\frac{1}{2}$ ${\log }_{2}x$

$\{{\log }_{a^k}x=\frac{1}{k}{\log }_{a}x\}$

(\log_4 x\) = $\frac{1}{2{\log }_{x}2}$

$\{{\log }_{a}x=\frac{1}{{\log }_{x}a}\}$
= $\frac{1}{2y}$

{Given ${\log }_{x}2$ = y}