Question

What would be the value of $x$ for the equation $2^x=\sqrt{2}$ ?

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

The correct option is A $\frac{1}{2}$

$2^x=\sqrt{2}$
$2^x=2^{\frac{1}{2}}\because [\sqrt{2}=2^{\frac{1}{2}}]$
Using laws of exponents,
Bases are same so, we can equate the exponents of the equation
$2^x=2^{\frac{1}{2}}$
Hence, $x=\frac{1}{2}$