Question

solve for x. enter your answer as a whole number or reduced fraction.

x = log₂√e

x =

Explanation:

Step1: Use logarithm property

By the logarithm property $\log_{a}b^c = c\log_{a}b$, for $x = \log_{e}\sqrt{e}$, since $\sqrt{e}=e^{\frac{1}{2}}$, we have $x=\log_{e}e^{\frac{1}{2}}$.

Step2: Use $\log_{a}a^k = k$

According to the formula $\log_{a}a^k = k$ (where $a = e$ and $k=\frac{1}{2}$), we get $x=\frac{1}{2}$.

Answer:

$\frac{1}{2}$