Question

What should be the value of $x$ such that the following equation is satisfied?
$2^6=4^x$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

If we wish to solve for $x$ in the equation $2^6=4^x,$ then we first need to make sure that the powers on both sides of the equation have equal bases.
We know that $2^2=4.$
$\therefore 4^x=(2^2{)}^x=2^{2x}(\because (a^m{)}^n=a^{mn})$
$\therefore 2^6=2^{2x}$
Since the bases of the powers on both sides of the equation are equal, the exponents must also be equal.
$⟹2x=6⟹x=3$