Respuesta :
Option B: [tex]x=\frac{8}{3}[/tex] is the solution
Explanation:
The given expression is [tex]\log _{2} 9 x-\log _{2} 3=3[/tex]
We need to determine the solution for the given expression.
The solution can be determined by solving the expression for x.
Adding [tex]\log _{2} 3[/tex] to both sides of the expression, we have,
[tex]\log _{2}9 x=3+\log _{2}3[/tex]
Using the logarithmic definition that if [tex]\log _{a}(b)=c[/tex] then [tex]b=a^{c}[/tex]
Thus, we have,
[tex]9 x=2^{3+\log _{2}3}[/tex]
[tex]9 x=2^{3}\cdot 2^{\log _{2}3}[/tex]
Simplifying, using the identity [tex]a^{\log _{a}(b)}=b[/tex], we have,
[tex]9 x=8\cdot 3[/tex]
Multiplying, we get,
[tex]9x=24[/tex]
Dividing both sides by 9, we have,
[tex]x=\frac{24}{9}[/tex]
Simplifying, we have,
[tex]x=\frac{8}{3}[/tex]
Thus, the solution of the expression is [tex]x=\frac{8}{3}[/tex]
