Answer: x = 64
Step-by-step explanation:
First you need to know that if we have: [tex]log_b(y)=x[/tex] this is equal to [tex]y=b^x[/tex]
So, [tex]log_x8=0.5[/tex] can be rewritten as: [tex]8=(x)^0^.^5[/tex]
[tex]0.5[/tex] can be rewritten as: [tex]\frac{1}{2}[/tex] and why did I do this? you may ask. This way I can rewrite the exponent as a square root, as following;
[tex]8=(x)^\frac{1}{2}[/tex]
The property says that: [tex]\sqrt[n]{x^m}=x^\frac{m}{n}[/tex]
So, we can rewrite our operation as;
[tex]8=\sqrt[]{x}[/tex]
Now let's raise both sides to the power of 2, to get rid of the square root.
[tex](8)^2=(\sqrt[]{x})^2[/tex]
[tex]64=x[/tex]
