Answer:
[tex] x = 36 [/tex]
Step-by-step explanation:
To find [tex] x [/tex] in the equation [tex] \log_x 6 = 0.5 [/tex], we'll use the definition of logarithms:
If [tex] \log_x y = z [/tex], then [tex] x^z = y [/tex].
So, in our equation:
[tex] \log_x 6 = 0.5 [/tex]
We rewrite this in exponential form:
[tex] x^{0.5} = 6 [/tex]
Now, to solve for [tex] x [/tex], we'll raise both sides of the equation to the power of 2:
[tex] (x^{0.5})^2 = 6^2 [/tex]
[tex] x^{0.5\cdot 2 } = 6^2 [/tex]
[tex] x = 6^2 [/tex]
[tex] x = 36 [/tex]
So, the value of [tex] x [/tex] is [tex] \boxed{36} [/tex].
