Question

If $lo{g}_{4}7=x$, then the value of $lo{g}_{7}16$ will be

• A. $x^2$
• B. $2x$
• C. $x$
• D. $\frac{2}{x}$

Answer 1

The correct option is D $\frac{2}{x}$

$\because lo{g}_{4}7=x$

$\Rightarrow 7=4^x$

$\Rightarrow 4=(7{)}^{1/x}$

$\therefore lo{g}_{7}16=lo{g}_7(4{)}^2$

$=2lo{g}_{7}4$

$=2lo{g}_7(7{)}^{1/x}$

$=2\frac{1}{x}\cdot lo{g}_{7}7$

$=2\cdot \frac{1}{x}\cdot 1$

$\frac{2}{x}$

Answer (D) $\frac{2}{x}$