Question

Match the following with the correct value of x in each of the below cases.

• A. 7
• B. 8
• C. 3
• D. 64

Answer 1

Case(1):

${\log }_{2}256=x$

$x=8{\log }_{2}2$

$x=8\times 1$

$x=8$

Case(2):

${\log }_{x}343=3$

${\log }_x{7}^3=3$

$3{\log }_{x}7=3$

${\log }_{x}7=1$

$x^1=7$

$x=7$

Case(3):

In exponential form, ${\log }_{4}x=3$
can be written as

$4^3=x$

$x=64$

Case(4):

${\log }_{3}4=\frac{1}{{\log }_{4}x}$

Since, ${\log }_{a}b=\frac{1}{{\log }_{b}a}$

So, $x=3$