Question

find the value of x.
\log_{x} 8 = 0.5
a. 4
b. 16
c. 32
d. 64

Explanation:

Step1: Convert log to exponential form

Recall the definition of a logarithm: if $\log_{a}b = c$, then $a^{c}=b$. For the equation $\log_{x}8 = 0.5$, we can rewrite it in exponential form as $x^{0.5}=8$.

Step2: Solve for x

Note that $x^{0.5}=\sqrt{x}$, so we have $\sqrt{x}=8$. To find $x$, we square both sides of the equation: $x = 8^{2}=64$.

Answer:

D. 64