Answer:
x = 1
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
Given
[tex]log_{64}[/tex] 8 = [tex]\frac{x}{2}[/tex] , then
8 = [tex]64^{\frac{x}{2} }[/tex]
note 64 = 8² , so
8 = [tex](8^2)^{\frac{x}{2} }[/tex] = [tex]8^{x}[/tex]
Since bases on both sides are equal, both 8 then equate the exponents
x = 1
