Respuesta :
The value of x is [tex]\frac{8}{3}[/tex]
Explanation:
The expression is [tex]\log _{2}(9 x)-\log _{2}(3)=3[/tex]
Adding [tex]\log _{2}(3)[/tex] to both sides of the equation, we get,
[tex]\log _{2}(9 x)=3+\log _{2}(3)[/tex]
Using log definition, if [tex]\log _{a}(b)=c[/tex] then [tex]b=a^{c}[/tex] , we have,
[tex]9 x=2^{3+\log _{2}(3)}[/tex]
Using exponent rule, [tex]a^{b+c}=a^{b} a^{c}[/tex],
[tex]9x=2^{\log _{2}(3)} \cdot 2^{3}[/tex]
Simplifying, we have,
[tex]9x=3\cdot8\\9x=24[/tex]
Dividing both sides by 9, we have,
[tex]x=\frac{24}{9}[/tex]
Simplifying,
[tex]x=\frac{8}{3}[/tex]
Thus, the value of x is [tex]\frac{8}{3}[/tex]
